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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Math worksheet on 'Radicals - Multiplying Binomials (Values and Variables) (Level 3)'. Part of a broader unit on 'Radicals - Multiplication Intro' Learn online: app.mobius.academy/math/units/radicals_multiplication_intro/
1
A LaTex expression showing (2pnsquare root of 11 - nsquare root of 11n) times (pnsquare root of 3pn - 4pnsquare root of 5p)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2{p} to the power of 2 {n} to the power of 2 square root of 33pn - p{n} to the power of 3 square root of 33p - 3{p} to the power of 2 {n} to the power of 2 square root of 55p + 4p{n} to the power of 2 square root of pn
b A LaTex expression showing 2{p} to the power of 2 {n} to the power of 2 square root of 33pn - p{n} to the power of 3 square root of 33 - 8{p} to the power of 2 {n} to the power of 2 square root of 55{p to the power of -1 } + 4p{n} to the power of 2 square root of 55pn
c A LaTex expression showing 2{p} to the power of 2 {n} to the power of 2 square root of 33pn - p{n} to the power of 3 square root of 33p + 8{p} to the power of 2 square root of 55p + 4p{n} to the power of 2 square root of 55p
d A LaTex expression showing 2{p} to the power of 2 {n} to the power of 2 square root of 33pn - p{n} to the power of 3 square root of 33p - 8{p} to the power of 2 {n} to the power of 2 square root of 55p + 4p{n} to the power of 2 square root of n
e A LaTex expression showing 2{p} to the power of 2 {n} to the power of 2 square root of 33pn - p{n} to the power of 3 square root of 33p - 8{p} to the power of 2 {n} to the power of 2 square root of 55p + 4p{n} to the power of 2 square root of 55pn
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 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
c 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 }
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 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 }
3
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 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
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 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
d 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
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
4
A LaTex expression showing ({y} to the power of 2 {c} to the power of 2 square root of 7 - 2ysquare root of 11) times ({y} to the power of 2 square root of 7c - 2square root of 7yc)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 7{y} to the power of 4 {c} to the power of 2 square root of c + 14y{c} to the power of 2 square root of y - 2{y} to the power of 3 square root of 77c + 4ysquare root of 77yc
b A LaTex expression showing 7{y} to the power of 4 {c} to the power of 2 square root of {c to the power of -1 } - 14{y} to the power of 2 {c} to the power of 2 square root of yc - 2{y} to the power of 3 square root of 77c + 4{y} to the power of -1 square root of 77yc
c A LaTex expression showing 7{y} to the power of 4 {c} to the power of 2 square root of c - 14{y} to the power of 2 {c} to the power of 3 square root of yc - 5{y} to the power of 3 square root of 77c - 4ysquare root of 77yc
d A LaTex expression showing 7{y} to the power of 4 {c} to the power of 2 square root of c - 14{y} to the power of 2 {c} to the power of 2 square root of yc - 2{y} to the power of 3 square root of 77c + 4ysquare root of 77yc
e A LaTex expression showing 7{y} to the power of 4 {c} to the power of 2 square root of c - 14{y} to the power of 2 {c} to the power of 2 square root of yc - 3{y} to the power of 3 square root of 77c + ysquare root of 77yc
5
A LaTex expression showing (square root of 3dn + 3{d} to the power of 2 nsquare root of 2) times (dnsquare root of 5dn - 3{n} to the power of 2 square root of 11)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 5{d} to the power of 2 {n} to the power of 2 square root of 15 - 3{n} to the power of 2 square root of 33dn + 3{d} to the power of 3 {n} to the power of 2 square root of 10n - 9{d} to the power of 2 {n} to the power of 3 square root of 22
b A LaTex expression showing {d} to the power of 2 {n} to the power of 2 square root of 15 - 3{n} to the power of 2 square root of 33dn + 3{d} to the power of 3 {n} to the power of 3 square root of 10n + 9{d} to the power of 2 {n} to the power of 3 square root of 22
c A LaTex expression showing {d} to the power of 2 {n} to the power of 2 square root of 15 - 2{n} to the power of 2 square root of 33dn + 3{d} to the power of 3 {n} to the power of 3 square root of 10dn - 9{d} to the power of 2 {n} to the power of 3 square root of 22
d A LaTex expression showing {d} to the power of 2 {n} to the power of 2 square root of 15d + {n} to the power of 2 square root of 33dn + 3{d} to the power of 3 {n} to the power of 2 square root of 10dn - 9{d} to the power of 2 {n} to the power of 3 square root of 22
e A LaTex expression showing {d} to the power of 2 {n} to the power of 2 square root of 15 - 3{n} to the power of 2 square root of 33dn + 3{d} to the power of 3 {n} to the power of 2 square root of 10dn - 9{d} to the power of 2 {n} to the power of 3 square root of 22
6
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 3 dsquare root of 21d
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 21d - 28pdsquare root of pd - {p} to the power of 3 dsquare root of 21d
c 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
d 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
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 d + 28{p} to the power of -1 dsquare root of pd - 8{p} to the power of 3 dsquare root of 21d
7
A LaTex expression showing (4dsquare root of 5 + rdsquare root of 7) times (r{d} to the power of 2 square root of 2 - 4square root of 2d)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 4{d} to the power of 4 rsquare root of 10 - 16dsquare root of 10d + {r} to the power of 2 {d} to the power of 3 square root of 14 - 4r{d} to the power of 2 square root of 14
b A LaTex expression showing 4{d} to the power of 3 {r} to the power of 5 square root of 10 - 16dsquare root of 10d + {r} to the power of 2 {d} to the power of 3 square root of 14 + 4rdsquare root of 14d
c A LaTex expression showing 4{d} to the power of 3 rsquare root of 10 - 16dsquare root of 10d + r{d} to the power of 3 square root of 14 - 4r{d} to the power of 2 square root of 14d
d A LaTex expression showing 4{d} to the power of 3 rsquare root of 10 - 16dsquare root of 10d + {r} to the power of 2 {d} to the power of 3 square root of 14 - 4rdsquare root of 14d
e A LaTex expression showing 4{d} to the power of 3 rsquare root of 10 - 16dsquare root of 10{d to the power of -1 } + {r} to the power of 2 {d} to the power of 3 square root of 14 - 4r{d} to the power of 2 square root of 14d