Multiplying Binomials (Values and Variables) (Level 3)

This math topic focuses on the skill of multiplying binomials involving both radicals and variables. Specifically, learners are required to multiply radical expressions, which may include coefficients and variable terms under different radical symbols, then simplify their results. The problems provided include complex expressions with varying degrees and types of radicals paired with algebraic variables, enhancing conceptual understanding and procedural skills in manipulations involving roots and powers. These types of problems are essential for understanding more advanced topics in algebra and precalculus.

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Radicals - Multiplying Binomials (Values and Variables) Worksheet

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Radicals - Multiplying Binomials (Values and Variables)
1
A LaTex expression showing (2bsquare root of 2b - {r} to the power of 2 square root of 11) times (3rsquare root of 11b + r{b} to the power of 2 square root of 7r)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 6r{b} to the power of 2 square root of 22b + 11{r} to the power of 3 square root of b - 2r{b} to the power of 3 square root of 14rb - {r} to the power of 3 {b} to the power of 2 square root of 77r
b A LaTex expression showing 6r{b} to the power of 2 square root of 22 - 22{r} to the power of 3 square root of {b to the power of -1 } + 2r{b} to the power of 3 square root of 14rb - {r} to the power of 3 {b} to the power of 2 square root of 77r
c A LaTex expression showing 6r{b} to the power of 2 square root of 22 - 33{r} to the power of 3 square root of b + 2r{b} to the power of 3 square root of 14rb - {r} to the power of 3 {b} to the power of 2 square root of 77r
d A LaTex expression showing 6r{b} to the power of 3 square root of 22 - 3{r} to the power of 3 square root of b + 2r{b} to the power of 3 square root of 14rb - {r} to the power of 3 {b} to the power of 2 square root of 77r
e A LaTex expression showing 6r{b} to the power of 3 square root of 22 - 11{r} to the power of 3 square root of b + 2r{b} to the power of 3 square root of 14rb + {r} to the power of 3 {b} to the power of 2 square root of 77r
2
A LaTex expression showing (2{z} to the power of 2 square root of 3 + rzsquare root of 7r) times (zsquare root of 7z - 2zsquare root of 11rz)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2{z} to the power of 3 square root of 21z - 4{z} to the power of 3 rsquare root of 33z + 7r{z} to the power of 2 square root of rz + 2{r} to the power of 2 {z} to the power of 3 square root of 77z
b A LaTex expression showing 2{z} to the power of 3 square root of 21z + 4{z} to the power of 3 square root of 33r{z to the power of -1 } + 7r{z} to the power of 2 square root of rz - 2{r} to the power of 2 {z} to the power of 2 square root of 77{z to the power of -1 }
c A LaTex expression showing 2{z} to the power of 3 square root of 21 - 4{z} to the power of 3 square root of 33rz + 7r{z} to the power of 2 square root of rz + 2{r} to the power of 2 {z} to the power of 2 square root of 77{z to the power of -1 }
d A LaTex expression showing 2{z} to the power of 3 square root of 21z - 4{z} to the power of 3 square root of 33rz + 7r{z} to the power of 2 square root of rz - 2{r} to the power of 2 {z} to the power of 2 square root of 77z
e A LaTex expression showing 2{z} to the power of 3 square root of 21z - 4{z} to the power of 3 square root of 33rz + 7r{z} to the power of 2 square root of rz + 5{r} to the power of 2 {z} to the power of 2 square root of 77z
3
A LaTex expression showing (2{r} to the power of 2 dsquare root of 3 - {d} to the power of 2 square root of 11) times (3dsquare root of 3r + {r} to the power of 2 {d} to the power of 2 square root of 7)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 18{d} to the power of 2 {r} to the power of 4 square root of r - 3{d} to the power of 3 square root of 33r + 2{r} to the power of 4 {d} to the power of 3 square root of 21 - {r} to the power of 2 {d} to the power of 4 square root of 77
b A LaTex expression showing 18{d} to the power of 2 {r} to the power of 2 - 3{d} to the power of 3 square root of 33r + 2{r} to the power of 2 {d} to the power of 3 square root of 21 - {r} to the power of 2 {d} to the power of 4 square root of 77
c A LaTex expression showing 18{d} to the power of 2 {r} to the power of 2 square root of {r to the power of -1 } - 3{d} to the power of 3 square root of 33r + 2{r} to the power of 4 {d} to the power of 3 square root of 21 - 2{r} to the power of 2 {d} to the power of 4 square root of 77
d A LaTex expression showing 18{d} to the power of 2 {r} to the power of 2 square root of r - {d} to the power of 3 square root of 33r + 2{r} to the power of 4 {d} to the power of 3 square root of 21 + {r} to the power of 2 {d} to the power of 4 square root of 77
e A LaTex expression showing 18{d} to the power of 2 {r} to the power of 2 square root of r - 3{d} to the power of 3 square root of 33r + 2{r} to the power of 4 {d} to the power of 3 square root of 21 - {r} to the power of 2 {d} to the power of 4 square root of 77
4
A LaTex expression showing (3{n} to the power of 2 {x} to the power of 2 square root of 7 - {n} to the power of 2 {x} to the power of 2 square root of 7) times (xsquare root of 5 - 4xsquare root of 3n)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2{x} to the power of 3 {n} to the power of 2 square root of 35 - 8{x} to the power of 3 {n} to the power of 2 square root of 21n
b A LaTex expression showing 3{x} to the power of 3 {n} to the power of 2 square root of 35 - {x} to the power of 3 {n} to the power of 2 + 12{x} to the power of 3 {n} to the power of 2 square root of 21n - 4{x} to the power of 3 {n} to the power of 2 square root of 21{n to the power of -1 }
c A LaTex expression showing 3{x} to the power of 3 {n} to the power of 2 square root of 35 - {x} to the power of 3 square root of 35 + 12{x} to the power of 3 {n} to the power of 2 square root of 21n - 4x{n} to the power of 2 square root of 21n
d A LaTex expression showing 2{x} to the power of 3 {n} to the power of 2 square root of 35 - 12{x} to the power of 3 {n} to the power of 2 square root of 21n + 4{x} to the power of 3 {n} to the power of 3 square root of 21
e A LaTex expression showing 3{x} to the power of 3 {n} to the power of 2 square root of 35 - {x} to the power of 3 nsquare root of 35 - 12{x} to the power of 3 {n} to the power of 2 square root of 21n + 4{x} to the power of 3 {n} to the power of 2 square root of 21
5
A LaTex expression showing ({p} to the power of 2 {d} to the power of 2 square root of 7 + 4psquare root of 7) times (dsquare root of 7pd - 2{p} to the power of 2 dsquare root of 3d)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 7{p} to the power of 2 {d} to the power of 3 square root of pd + 2{p} to the power of 4 {d} to the power of 3 square root of 21d - 28pdsquare root of pd - 8{p} to the power of 5 dsquare root of 3d
b A LaTex expression showing 7{p} to the power of 2 {d} to the power of 3 square root of pd - 2{p} to the power of 4 {d} to the power of 3 square root of d + 28{p} to the power of -1 dsquare root of pd - 8{p} to the power of 3 dsquare root of 21d
c A LaTex expression showing 7{p} to the power of 5 {d} to the power of 3 square root of pd - 2{p} to the power of 4 {d} to the power of 3 square root of 21d - 28pdsquare root of pd - 8{p} to the power of 3 dsquare root of 21d
d A LaTex expression showing 7{p} to the power of 2 {d} to the power of 3 square root of pd - 2{p} to the power of 4 {d} to the power of 3 square root of 21d - 28pdsquare root of pd - {p} to the power of 3 dsquare root of 21d
e A LaTex expression showing 7{p} to the power of 2 {d} to the power of 3 square root of pd - 2{p} to the power of 4 {d} to the power of 3 square root of 21d + 28pdsquare root of pd - 8{p} to the power of 3 dsquare root of 21d
6
A LaTex expression showing (2n{p} to the power of 2 square root of 3n + {n} to the power of 2 psquare root of 2p) times ({n} to the power of 2 square root of 13p - 5{n} to the power of 2 psquare root of 7)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2{n} to the power of 4 {p} to the power of 2 square root of 39p - 10{n} to the power of 3 {p} to the power of 3 square root of 21n - {n} to the power of 4 psquare root of 26 + 5{n} to the power of 4 {p} to the power of 2 square root of 14p
b A LaTex expression showing 2{n} to the power of 3 {p} to the power of 2 square root of 39np - 10{n} to the power of 3 {p} to the power of 3 square root of 21n + {n} to the power of 4 {p} to the power of 2 square root of 26 - {n} to the power of 4 psquare root of 14p
c A LaTex expression showing 2{n} to the power of 3 {p} to the power of 2 square root of 39np - 10{n} to the power of 4 {p} to the power of 3 square root of 21n + {n} to the power of 4 {p} to the power of 2 square root of 26 - 5{n} to the power of 4 {p} to the power of 2 square root of 14
d A LaTex expression showing 2{n} to the power of 3 {p} to the power of 2 square root of 39np - 10{n} to the power of 3 {p} to the power of 3 - {n} to the power of 4 {p} to the power of 2 square root of 26 - 5{n} to the power of 4 {p} to the power of 2 square root of 14p
e A LaTex expression showing 2{n} to the power of 3 {p} to the power of 2 square root of 39np - 10{n} to the power of 3 {p} to the power of 3 square root of 21n + {n} to the power of 4 {p} to the power of 2 square root of 26 - 5{n} to the power of 4 {p} to the power of 2 square root of 14p
7
A LaTex expression showing (3square root of 13mp + mpsquare root of 2p) times (mpsquare root of 7p - 2mpsquare root of 3p)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 3m{p} to the power of 2 square root of 91m - 2{m} to the power of 2 {p} to the power of 3 square root of 14 - 6{m} to the power of 2 {p} to the power of 2 square root of 39m + 2{m} to the power of 2 {p} to the power of 3 square root of 6
b A LaTex expression showing 3m{p} to the power of 2 square root of 91m + m{p} to the power of 2 square root of 14p + 6m{p} to the power of 2 square root of 39m - 2{m} to the power of 2 {p} to the power of 3 square root of 6
c A LaTex expression showing 3m{p} to the power of 2 square root of 91m + {m} to the power of 2 {p} to the power of 3 square root of 14p - 6m{p} to the power of 2 square root of 39m - 2{m} to the power of 2 {p} to the power of 3 square root of 2
d A LaTex expression showing 3m{p} to the power of 2 square root of 91m + {m} to the power of 2 {p} to the power of 5 square root of 14 - 6m{p} to the power of 2 square root of 39m - 2{m} to the power of 2 {p} to the power of 4 square root of 6
e A LaTex expression showing 3m{p} to the power of 2 square root of 91m + {m} to the power of 2 {p} to the power of 3 square root of 14 - 6m{p} to the power of 2 square root of 39m - 2{m} to the power of 2 {p} to the power of 3 square root of 6
8
A LaTex expression showing (5bsquare root of 7d - bsquare root of 7d) times (d{b} to the power of 2 square root of 13d + 2{d} to the power of 2 bsquare root of 5)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 4{d} to the power of 2 {b} to the power of 3 square root of 91 - 10{d} to the power of 3 {b} to the power of 2 square root of 35d - 5{d} to the power of 2 {b} to the power of 2 square root of 35d
b A LaTex expression showing 12{d} to the power of 2 {b} to the power of 2 square root of 35d
c A LaTex expression showing 4{d} to the power of 2 {b} to the power of 3 square root of 91 - 12{d} to the power of 2 {b} to the power of 2 square root of 35d
d A LaTex expression showing 6{d} to the power of 2 {b} to the power of 3 square root of 91 + 10{d} to the power of 2 {b} to the power of 2 square root of 35d - 2{d} to the power of 2 {b} to the power of 4 square root of d
e A LaTex expression showing 5{d} to the power of 2 {b} to the power of 3 square root of 91 - {d} to the power of 2 {b} to the power of 3 square root of 91d + 10{d} to the power of 2 {b} to the power of 2 square root of 35d - 2{d} to the power of 2 {b} to the power of 2 square root of 35