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Radicals - 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.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Multiplying Binomials (Values and Variables)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Multiply the radical expressions and simplify the answer

(2cr13cr+c213)⋅(2c3c+r22)(2cr\sqrt{13cr} + {c}^{2}\sqrt{13}) \cdot (2c\sqrt{3c} + {r}^{2}\sqrt{2})

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 (2c{x} to the power of 2 square root of 5 - c{x} to the power of 2 square root of 5) times ({c} to the power of 2 xsquare root of 3 + 4xsquare root of 5cx)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2{c} to the power of 3 {x} to the power of 3 square root of 15 + 60c{x} to the power of 3 square root of cx
b A LaTex expression showing 2{c} to the power of 3 {x} to the power of 2 square root of 15 + 20c{x} to the power of 3 square root of cx + {c} to the power of 3 {x} to the power of 3 square root of 15
c A LaTex expression showing {c} to the power of 3 {x} to the power of 3 square root of 15 - 7c{x} to the power of 3 square root of cx
d A LaTex expression showing {c} to the power of 3 {x} to the power of 3 square root of 15 + 20c{x} to the power of 3 square root of cx
e A LaTex expression showing 2{c} to the power of 3 {x} to the power of 3 square root of 15 + 40c{x} to the power of 3 square root of {c to the power of -1 x} + {c} to the power of 3 {x} to the power of 3 - 20c{x} to the power of 3 square root of cx
f A LaTex expression showing {c} to the power of 4 {x} to the power of 3 square root of 15 + 60c{x} to the power of 3 square root of cx - {c} to the power of 3 {x} to the power of 3 square root of 15
2
A LaTex expression showing (psquare root of 7 - 4square root of 5) times (z{p} to the power of 2 square root of 7z + 3psquare root of 2)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 7{p} to the power of 3 zsquare root of z - 3{p} to the power of 2 square root of 14 - 4z{p} to the power of 2 square root of 35z + 4{p} to the power of -1 square root of 10
b A LaTex expression showing 7{p} to the power of 3 zsquare root of {z to the power of -1 } + 3{p} to the power of 2 square root of 14 - 4{z} to the power of 2 {p} to the power of 2 square root of 35 + 12psquare root of 10
c A LaTex expression showing 7{p} to the power of 3 zsquare root of z + 3{p} to the power of 2 square root of 14 - 4z{p} to the power of 2 square root of 35z - 12psquare root of 10
d A LaTex expression showing 7{p} to the power of 3 zsquare root of z + 3{p} to the power of 2 square root of 14 - z{p} to the power of 2 square root of 35z - 12p
e A LaTex expression showing 7{p} to the power of 3 zsquare root of {z to the power of -1 } - 3psquare root of 14 + 4z{p} to the power of 2 square root of 35z - 12psquare root of 10
f A LaTex expression showing {p} to the power of 3 {z} to the power of -1 square root of z + 3{p} to the power of 2 square root of 14 - 4z{p} to the power of 2 square root of 35z - 12psquare root of 10
3
A LaTex expression showing (4nsquare root of 2m - {m} to the power of 2 {n} to the power of 2 square root of 3) times ({m} to the power of 2 {n} to the power of 2 square root of 2 + 4{m} to the power of 2 square root of 2n)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 8{m} to the power of 2 {n} to the power of 3 square root of m + {m} to the power of 4 {n} to the power of 4 square root of 6 + 32{m} to the power of 2 nsquare root of nm - 4{m} to the power of 6 {n} to the power of 2 square root of 6
b A LaTex expression showing 8{m} to the power of 3 {n} to the power of 3 square root of m - 2{m} to the power of 4 {n} to the power of 4 + 32{m} to the power of 2 nsquare root of nm - 4{m} to the power of 4 {n} to the power of 2 square root of 6n
c A LaTex expression showing 8{m} to the power of 2 {n} to the power of 3 square root of m - {m} to the power of 4 {n} to the power of 4 square root of 6 + 2{m} to the power of 2 nsquare root of nm + 4{m} to the power of 4 {n} to the power of 2 square root of 6
d A LaTex expression showing 8m{n} to the power of 3 square root of m - {m} to the power of 4 {n} to the power of 4 square root of 6 + 32{m} to the power of 3 nsquare root of n - 4{m} to the power of 4 {n} to the power of 2 square root of 6n
e A LaTex expression showing 8{m} to the power of 2 {n} to the power of 3 square root of m + 3{m} to the power of 4 {n} to the power of 4 square root of 6 + 32{m} to the power of 2 nsquare root of nm
f A LaTex expression showing 8{m} to the power of 2 {n} to the power of 3 square root of m - {m} to the power of 4 {n} to the power of 4 square root of 6 + 32{m} to the power of 2 nsquare root of nm - 4{m} to the power of 4 {n} to the power of 2 square root of 6n
4
A LaTex expression showing ({z} to the power of 2 msquare root of 13 + 4msquare root of 2) times (square root of 13z + 2zmsquare root of 5)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 13{z} to the power of 2 msquare root of z - 2z{m} to the power of 2 + 4msquare root of 26z + 8{m} to the power of 2 zsquare root of 10
b A LaTex expression showing 2{z} to the power of 2 msquare root of z + 2{z} to the power of 3 {m} to the power of 2 square root of 65 + 4msquare root of 26z + 8{m} to the power of 2 zsquare root of 10
c A LaTex expression showing 13{z} to the power of 2 msquare root of z + 2{z} to the power of 3 {m} to the power of 2 square root of 65 + 4msquare root of 26z + 8{m} to the power of 2 zsquare root of 10
d A LaTex expression showing 13{z} to the power of 2 msquare root of z + 2{z} to the power of 3 {m} to the power of 2 square root of 65 - square root of 26z + 8{m} to the power of 2 zsquare root of 10
e A LaTex expression showing 13{z} to the power of 2 {m} to the power of 3 square root of z + 2{z} to the power of 3 {m} to the power of 2 square root of 65 + 4msquare root of z - 8{m} to the power of 2 zsquare root of 10
f A LaTex expression showing 13{z} to the power of 2 msquare root of z + 2{z} to the power of 3 {m} to the power of 2 - 4msquare root of 26 + 8{m} to the power of 2 zsquare root of 10
5
A LaTex expression showing (csquare root of 5y + 3csquare root of 13) times (csquare root of 2 - 2ysquare root of 5c)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {c} to the power of 3 square root of 10y - 10cysquare root of yc + {c} to the power of 2 square root of 26 + 6cysquare root of 65c
b A LaTex expression showing {c} to the power of 2 square root of 10y - 10cysquare root of yc + 3{c} to the power of 2 square root of 26 - 6cysquare root of 65c
c A LaTex expression showing {c} to the power of 2 square root of 10y - 2cysquare root of yc + 3square root of 26 + 6cysquare root of 65c
d A LaTex expression showing {c} to the power of 2 square root of 10y - 10cysquare root of yc + 3csquare root of 26 + 6cysquare root of 65
e A LaTex expression showing {c} to the power of 2 square root of 10y - 10cysquare root of yc + 3{c} to the power of 2 square root of 26 - c{y} to the power of 2 square root of 65c
f A LaTex expression showing {c} to the power of 2 square root of 10y - 10cysquare root of yc + 3{c} to the power of 2 square root of 26 - 5cysquare root of 65c
6
A LaTex expression showing ({d} to the power of 2 bsquare root of 3 - 3square root of 3b) times ({d} to the power of 2 bsquare root of 13b - 4{d} to the power of 2 bsquare root of 7b)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {d} to the power of 4 {b} to the power of 2 square root of 39b - 4{d} to the power of 4 {b} to the power of 2 square root of 21b - 3{d} to the power of 2 {b} to the power of 2 square root of 39b + 12{d} to the power of 2 {b} to the power of 2 square root of 21
b A LaTex expression showing {d} to the power of 4 {b} to the power of 2 square root of 39b - 4{d} to the power of 4 {b} to the power of 2 square root of 21b - 3{d} to the power of 2 {b} to the power of 2 square root of 39 + 12{d} to the power of 2 {b} to the power of 2 square root of 21
c A LaTex expression showing {d} to the power of 4 bsquare root of 39b - 4{d} to the power of 4 {b} to the power of 2 square root of 21b - 3{d} to the power of 2 {b} to the power of 2 square root of 39 + 12{d} to the power of 2 bsquare root of 21
d A LaTex expression showing {d} to the power of 5 {b} to the power of 2 square root of 39b - 4{d} to the power of 4 {b} to the power of 2 square root of 21b + 3{d} to the power of 2 {b} to the power of 3 square root of 39 - 12{d} to the power of 2 {b} to the power of 2 square root of 21
e A LaTex expression showing {d} to the power of 4 {b} to the power of 2 square root of 39b - 4{d} to the power of 4 {b} to the power of 2 square root of 21b - 3d{b} to the power of 2 square root of 39 + 12{d} to the power of 2 {b} to the power of 3 square root of 21
f A LaTex expression showing {d} to the power of 4 {b} to the power of 2 square root of 39b - 4{d} to the power of 4 {b} to the power of 3 square root of 21 - 3{d} to the power of 2 {b} to the power of 2 square root of 39 + 12{d} to the power of 2 {b} to the power of 4 square root of 21
7
A LaTex expression showing (pxsquare root of 7p + 5{p} to the power of 2 square root of 11x) times (pxsquare root of 5px + 3pxsquare root of 2)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {p} to the power of 3 {x} to the power of 2 square root of x + 3{p} to the power of 2 {x} to the power of 2 square root of 14p + 5{p} to the power of 3 {x} to the power of 2 square root of 55p + 30{p} to the power of 3 xsquare root of x
b A LaTex expression showing {p} to the power of 3 {x} to the power of 2 square root of 2x + 3{p} to the power of 2 {x} to the power of 2 square root of 14p - 5{p} to the power of 3 {x} to the power of 2 square root of 55p + 15{p} to the power of 3 {x} to the power of 2 square root of 22
c A LaTex expression showing {p} to the power of 3 {x} to the power of 2 square root of 35x + {p} to the power of 2 {x} to the power of 2 square root of 14p - 5{p} to the power of 3 {x} to the power of 3 square root of 55p + 15{p} to the power of 3 xsquare root of 22x
d A LaTex expression showing {p} to the power of 3 {x} to the power of 2 square root of 35x + 3{p} to the power of 3 {x} to the power of 2 square root of 14p + 5{p} to the power of 3 {x} to the power of 2 square root of 55 + 15{p} to the power of 3 xsquare root of 22x
e A LaTex expression showing {p} to the power of 3 {x} to the power of 2 square root of 35x + 3{p} to the power of 2 {x} to the power of 2 square root of 14p + 5{p} to the power of 3 {x} to the power of 2 square root of 55p + 15{p} to the power of 3 xsquare root of 22x
f A LaTex expression showing {p} to the power of 3 {x} to the power of 2 square root of 35x + {p} to the power of 2 {x} to the power of 2 square root of 14p + 5{p} to the power of 3 {x} to the power of 2 square root of 55p + 15{p} to the power of 3 {x} to the power of 2 square root of 22x