Multiplying Binomials (Values and Variables) (Level 2)

This math topic focuses on practicing the multiplication of binomial expressions that contain radicals, involving variables and constants. It covers expanding and simplifying the products of binomial expressions which comprise square roots and variable terms at a more advanced level, possibly including the distribution of squared and cubed terms. Each problem sets up expressions in a format inviting the student to carry out the multiplication and then choose the correctly simplified form from multiple choices, ensuring a comprehensive understanding and application of radical manipulation rules in algebra.

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

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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 ({z} to the power of 2 square root of 2 + zsquare root of 13z) times (zsquare root of 2z - zsquare root of 13)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 2{z} to the power of 4 - 65{z} to the power of 2 square root of z
b A LaTex expression showing 2{z} to the power of 3 square root of z + 13{z} to the power of 4 square root of z
c A LaTex expression showing 2zsquare root of z - 13{z} to the power of 3
d A LaTex expression showing 2{z} to the power of 3 square root of z - 13{z} to the power of 2 square root of z
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing (bsquare root of 7 + square root of 5) times (square root of 3b + square root of 5b)
a A LaTex expression showing square root of 21b - square root of 15b + bsquare root of 35 + 5square root of b
b A LaTex expression showing {b} to the power of 2 square root of 21b + square root of 15b + {b} to the power of 3 square root of 35b - 5square root of b
c A LaTex expression showing bsquare root of 21{b to the power of -1 } + 6square root of b + bsquare root of 35b
d A LaTex expression showing bsquare root of 21b + square root of 15b + bsquare root of 35b + 5square root of b
e A LaTex expression showing bsquare root of 21b + square root of 15b + {b} to the power of -1 square root of 35b + square root of b
3
A LaTex expression showing (msquare root of 3 - {m} to the power of 2 square root of 2) times (square root of 7m + {m} to the power of 2 square root of 13)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing msquare root of 21m - {m} to the power of 3 square root of 14 + msquare root of 39 - {m} to the power of 4 square root of 26
b A LaTex expression showing msquare root of 21m - {m} to the power of 3 square root of 14m - {m} to the power of 3 square root of 39 + {m} to the power of 4 square root of 26
c A LaTex expression showing {m} to the power of 3 square root of 21m - {m} to the power of 2 square root of 14m + 5{m} to the power of 3 square root of 39 - {m} to the power of 4 square root of 26
d A LaTex expression showing msquare root of 21m - {m} to the power of 2 square root of 14m + {m} to the power of 3 square root of 39 - {m} to the power of 4 square root of 26
e A LaTex expression showing msquare root of 21m + {m} to the power of 3 square root of 14m - {m} to the power of 3 square root of 39 - 3{m} to the power of 4 square root of 26
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 3 - ysquare root of 5) times (ysquare root of 7y + square root of 13)
a A LaTex expression showing ysquare root of 21y + square root of 39 - {y} to the power of 2 square root of 35y - ysquare root of 65
b A LaTex expression showing {y} to the power of 2 square root of 21y + square root of 39 - {y} to the power of 3 square root of 35 - ysquare root of 65
c A LaTex expression showing ysquare root of 21y - 2square root of 39 + {y} to the power of 2 square root of 35y - ysquare root of 65
d A LaTex expression showing ysquare root of 21y + 1 + {y} to the power of 3 square root of 35y - ysquare root of 65
5
A LaTex expression showing ({z} to the power of 2 square root of 13 - zsquare root of 11z) times (zsquare root of 11 - zsquare root of 13)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {z} to the power of 3 square root of 143 - 13{z} to the power of 5 - 11{z} to the power of 2 square root of z + {z} to the power of 2 square root of 143z
b A LaTex expression showing {z} to the power of 3 square root of 143 - 13{z} to the power of 3 - 11{z} to the power of 2 square root of z + {z} to the power of 2 square root of 143z
c A LaTex expression showing {z} to the power of 5 square root of 143 + 13{z} to the power of 2 - 11{z} to the power of 2 square root of z + {z} to the power of 2 square root of 143z
d A LaTex expression showing {z} to the power of 3 square root of 143 + 2{z} to the power of 3 - {z} to the power of 2 square root of 143z
6
A LaTex expression showing (square root of 2x + square root of 11) times (xsquare root of 13 - xsquare root of 7x)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing xsquare root of 26x - {x} to the power of 2 square root of 14 + 2xsquare root of 143 - xsquare root of 77x
b A LaTex expression showing xsquare root of 26x - {x} to the power of 2 square root of 14 + {x} to the power of 2 square root of 143 - xsquare root of 77x
c A LaTex expression showing xsquare root of 26x - {x} to the power of 2 square root of 14 + xsquare root of 143 - xsquare root of 77x
d A LaTex expression showing xsquare root of 26 + {x} to the power of 2 square root of 14 + xsquare root of 143 - xsquare root of 77x
e A LaTex expression showing {x} to the power of 2 square root of 26x - {x} to the power of 2 square root of 14 + xsquare root of 143 - {x} to the power of 2 square root of 77x
7
A LaTex expression showing (msquare root of 5 - {m} to the power of 2 square root of 7) times (square root of 11m + msquare root of 2m)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {m} to the power of 2 square root of 55m + {m} to the power of 2 square root of 10m - {m} to the power of 2 square root of 77m + {m} to the power of 3 square root of 14
b A LaTex expression showing msquare root of 55 + {m} to the power of 2 square root of 10m - {m} to the power of 3 square root of 77m - {m} to the power of 3 square root of 14m
c A LaTex expression showing msquare root of 55m + {m} to the power of 2 square root of 10m - {m} to the power of 2 square root of 77m - {m} to the power of 3 square root of 14m
d A LaTex expression showing msquare root of 55m + {m} to the power of 2 square root of 10m - {m} to the power of 2 square root of 77m - 5{m} to the power of 3 square root of 14m
e A LaTex expression showing msquare root of 55m + {m} to the power of 2 square root of 10m + {m} to the power of 4 square root of 77m - {m} to the power of 4 square root of 14m
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing ({z} to the power of 2 square root of 11 + square root of 13) times (zsquare root of 2 + square root of 3)
a A LaTex expression showing {z} to the power of 3 square root of 22 + {z} to the power of 2 square root of 33 + zsquare root of 26 + square root of 39
b A LaTex expression showing {z} to the power of 3 square root of 22 + 4{z} to the power of 2 square root of 33 + square root of 26 - square root of 39
c A LaTex expression showing {z} to the power of 3 square root of 22 + {z} to the power of 2 square root of 33 - {z} to the power of 2 square root of 26 + square root of 39
d A LaTex expression showing {z} to the power of 3 - {z} to the power of 2 square root of 33 + zsquare root of 26 + square root of 39
e A LaTex expression showing {z} to the power of 4 square root of 22 + {z} to the power of 2 square root of 33 + {z} to the power of -1 square root of 26 + square root of 39