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Radicals - 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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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

(7−z5)⋅(13−z7)(\sqrt{7} - z\sqrt{5}) \cdot (\sqrt{13} - z\sqrt{7})

Radicals - Multiplying Binomials (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Multiplying Binomials (Values and Variables) (Level 2)'. Part of a broader unit on 'Radicals - Multiplication Intro' Learn online: app.mobius.academy/math/units/radicals_multiplication_intro/
1
A LaTex expression showing ({x} to the power of 2 square root of 7 - square root of 2) times (xsquare root of 11 + xsquare root of 2x)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {x} to the power of 3 square root of 77 - xsquare root of 22 + {x} to the power of 3 square root of 14{x to the power of -1 } + 2{x} to the power of 2 square root of x
b A LaTex expression showing {x} to the power of 3 square root of 77 - xsquare root of 22 + {x} to the power of 3 square root of 14{x to the power of -1 } - 2xsquare root of x
c A LaTex expression showing {x} to the power of 3 square root of 77 - xsquare root of 22 + {x} to the power of 4 square root of 14 + 2square root of x
d A LaTex expression showing {x} to the power of 3 square root of 77 - xsquare root of 22 + {x} to the power of 2 square root of 14 - 2xsquare root of x
e A LaTex expression showing {x} to the power of 3 square root of 77 - {x} to the power of 2 square root of 22 - {x} to the power of 3 square root of 14x + 2xsquare root of x
f A LaTex expression showing {x} to the power of 3 square root of 77 - xsquare root of 22 + {x} to the power of 3 square root of 14x - 2xsquare root of x
2
A LaTex expression showing (rsquare root of 11r - {r} to the power of 2 square root of 3) times (rsquare root of 2r + {r} to the power of 2 square root of 2)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {r} to the power of 3 square root of 22r + {r} to the power of 3 square root of r - {r} to the power of 3 square root of 6r + {r} to the power of 4 square root of 6
b A LaTex expression showing {r} to the power of 3 square root of 3 + {r} to the power of 3 square root of 22r - {r} to the power of 3 square root of 6 + {r} to the power of 4 square root of 6
c A LaTex expression showing {r} to the power of 3 square root of 22 + {r} to the power of 3 square root of 22r - {r} to the power of 3 square root of 6r - {r} to the power of 4 square root of 6
d A LaTex expression showing {r} to the power of 4 square root of 22 + {r} to the power of 3 square root of 22r + {r} to the power of 3 square root of 6r - {r} to the power of 4 square root of 6
e A LaTex expression showing {r} to the power of 3 square root of 22 + rsquare root of 22r - {r} to the power of 3 square root of 6r - {r} to the power of 6 square root of 6
f A LaTex expression showing {r} to the power of 4 square root of 22 + {r} to the power of 3 square root of 22r - {r} to the power of 3 square root of 6r - {r} to the power of 4 square root of 6
3
A LaTex expression showing (msquare root of 11 + {m} to the power of 2 square root of 11) times (square root of 13 + msquare root of 11)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing msquare root of 143 + {m} to the power of 2 square root of 143 - 11{m} to the power of 2 + 11{m} to the power of 4
b A LaTex expression showing msquare root of 143 + 10{m} to the power of 2 + 11{m} to the power of 3
c A LaTex expression showing msquare root of 143 + {m} to the power of 2 square root of 143 + 11{m} to the power of 2 + 11{m} to the power of 3
d A LaTex expression showing msquare root of 143 + 11{m} to the power of 3
e A LaTex expression showing square root of 143 - msquare root of 143 + 11{m} to the power of 2 + 11{m} to the power of 3
f A LaTex expression showing msquare root of 143 + 12{m} to the power of 2 + 11m
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing ({x} to the power of 2 square root of 2 + xsquare root of 3x) times (square root of 2 - square root of 3x)
a A LaTex expression showing 5{x} to the power of 2 + {x} to the power of 2 square root of 6x - {x} to the power of 2 square root of x
b A LaTex expression showing 2{x} to the power of 2 + xsquare root of 6x + {x} to the power of 2 square root of 6x - 3{x} to the power of 3 square root of x
c A LaTex expression showing -1{x} to the power of 2 + {x} to the power of 3 square root of 6{x to the power of -1 } + {x} to the power of 2 square root of 6x
d A LaTex expression showing 5{x} to the power of 2 + xsquare root of 6x - {x} to the power of 2 square root of 6x
e A LaTex expression showing -1{x} to the power of 2 - xsquare root of 6x - {x} to the power of 2 square root of 6x
f A LaTex expression showing -1{x} to the power of 2 + xsquare root of 6x - {x} to the power of 2 square root of 6x
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 7 - zsquare root of 5) times (square root of 13 - zsquare root of 7)
a A LaTex expression showing square root of 91 + 7z - square root of 65 - {z} to the power of 2 square root of 35
b A LaTex expression showing square root of 91 + 7z - zsquare root of 65 + {z} to the power of 2 square root of 35
c A LaTex expression showing square root of 91 - 7z - zsquare root of 65 + {z} to the power of 2 square root of 35
d A LaTex expression showing 4square root of 91 - 7z + {z} to the power of 3 square root of 65 + {z} to the power of 2 square root of 35
e A LaTex expression showing square root of 91 - 7z - zsquare root of 65 + {z} to the power of 4 square root of 35
f A LaTex expression showing square root of 91 + 7z - zsquare root of 65 - {z} to the power of 3 square root of 35
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing (csquare root of 5 - {c} to the power of 2 square root of 3) times ({c} to the power of 2 square root of 3 + csquare root of 5)
a A LaTex expression showing {c} to the power of 3 square root of 15 + 3{c} to the power of 4 + 5{c} to the power of 2 - csquare root of 15
b A LaTex expression showing 2{c} to the power of 3 - 3{c} to the power of 4 + 5{c} to the power of 2 - {c} to the power of 3 square root of 15
c A LaTex expression showing 3{c} to the power of 4 + 5{c} to the power of 2
d A LaTex expression showing 2{c} to the power of 3 square root of 15 - 3{c} to the power of 3 + {c} to the power of 2 square root of 2
e A LaTex expression showing 2{c} to the power of 3 square root of 15 - 3{c} to the power of 3 + 5
f A LaTex expression showing 2{c} to the power of 3 square root of 15 - 3{c} to the power of 4 + 5{c} to the power of 2
7
A LaTex expression showing (zsquare root of 2z + zsquare root of 2) times (square root of 13 + {z} to the power of 2 square root of 11)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing zsquare root of 26z + zsquare root of 26 + {z} to the power of 3 square root of 22z + {z} to the power of 3 square root of 22
b A LaTex expression showing 2zsquare root of 26 + {z} to the power of 3 square root of 22z - 5{z} to the power of 3 square root of 22
c A LaTex expression showing zsquare root of z + zsquare root of 26 + zsquare root of 22z + {z} to the power of 3 square root of 22
d A LaTex expression showing zsquare root of 26z - zsquare root of 26 + {z} to the power of 2 square root of 22z + zsquare root of 22
e A LaTex expression showing zsquare root of 26z + zsquare root of 26 + {z} to the power of 3 square root of z - {z} to the power of 3 square root of 22
f A LaTex expression showing zsquare root of 26z + zsquare root of 26 + {z} to the power of 3 square root of 22z - {z} to the power of 3 square root of 22