Multiplying Binomials (Values and Variables) (Level 1)

This math topic focuses on practicing the multiplication of radical expressions involving binomials that include both numerical and variable components. The skills developed entail expanding and simplifying algebraic expressions that feature radicals and a variety of operations such as addition, subtraction, and multiplication. Each problem is presented with multiple-choice answers for students to select the correctly simplified version of the radical product. The main theme of these problems is not only to perform the multiplication accurately but also to apply the rules for simplifying square roots and combining like terms.

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
Multiply the radical expressions and simplify the answer
A LaTex expression showing (square root of 7r + 4r) times ({r} to the power of 2 square root of 5 - 4r)
a A LaTex expression showing rsquare root of 35r - 4{r} to the power of 2 square root of 7r + 4{r} to the power of 3 square root of 5 - 16{r} to the power of 2
b A LaTex expression showing {r} to the power of 2 square root of 35{r to the power of -1 } - 4{r} to the power of 2 square root of 7 + 4{r} to the power of 3 square root of 5 - 16{r} to the power of 2
c A LaTex expression showing {r} to the power of 2 square root of r + 4rsquare root of 7r - {r} to the power of 3 square root of 5 - 16{r} to the power of 2
d A LaTex expression showing {r} to the power of 2 square root of 35r - 4rsquare root of 7r + 4{r} to the power of 3 square root of 5 - 16{r} to the power of 2
e A LaTex expression showing {r} to the power of 4 square root of 35r + 4rsquare root of 7 + 4{r} to the power of 3 square root of 5 - 16{r} to the power of 2
2
A LaTex expression showing (4xsquare root of x - {x} to the power of 2 square root of 5) times (3{x} to the power of 2 + xsquare root of 13)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 12{x} to the power of 3 square root of x + 3{x} to the power of 4 square root of 5 + 4{x} to the power of 2 square root of 13x - 5{x} to the power of 5 square root of 65
b A LaTex expression showing 12{x} to the power of 3 square root of x - 3{x} to the power of 4 square root of 5 + 4{x} to the power of 2 square root of 13x - {x} to the power of 3 square root of 65
c A LaTex expression showing 12{x} to the power of 3 square root of x - 3{x} to the power of 4 square root of 5 + 4{x} to the power of 3 square root of 13x + {x} to the power of 3 square root of 65
d A LaTex expression showing 12{x} to the power of 3 square root of x - 3{x} to the power of 5 square root of 5 + 4{x} to the power of 2 square root of 13x + {x} to the power of 3
e A LaTex expression showing 12{x} to the power of 3 square root of x - 3{x} to the power of 4 square root of 5 - 4{x} to the power of 2 square root of 13x - 3{x} to the power of 5 square root of 65
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing (5rsquare root of r - square root of 5r) times (rsquare root of 11r - 3{r} to the power of 2 )
a A LaTex expression showing 5{r} to the power of 3 square root of 11 - 15{r} to the power of 3 square root of r + rsquare root of 55r + 3{r} to the power of 4 square root of 5r
b A LaTex expression showing 5{r} to the power of 3 square root of 11 - {r} to the power of 3 square root of r - {r} to the power of 2 square root of 55 + 3{r} to the power of 2 square root of 5{r to the power of -1 }
c A LaTex expression showing 5{r} to the power of 2 square root of 11 - 15{r} to the power of 3 square root of {r to the power of -1 } - {r} to the power of 2 square root of 55 + 3{r} to the power of 2 square root of 5r
d A LaTex expression showing 5{r} to the power of 3 square root of 11 - 15{r} to the power of 3 square root of r - {r} to the power of 2 square root of 55 + 3{r} to the power of 2 square root of 5r
e A LaTex expression showing 5{r} to the power of 3 square root of 11 - 15{r} to the power of 3 square root of r - {r} to the power of 2 square root of 55 + 3square root of 5
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3r + {r} to the power of 2 square root of 2) times (4rsquare root of r - square root of 13r)
a A LaTex expression showing 12{r} to the power of 2 square root of r + 4{r} to the power of 3 square root of 2r - 3rsquare root of 13r - {r} to the power of 2 square root of 26r
b A LaTex expression showing {r} to the power of 3 - 4{r} to the power of 3 square root of 2r - 3rsquare root of 13r - {r} to the power of 2 square root of 26r
c A LaTex expression showing 12{r} to the power of 2 square root of r + 4{r} to the power of 4 square root of 2r - 3rsquare root of 13r - {r} to the power of 2 square root of 26r
d A LaTex expression showing 12{r} to the power of 3 square root of r + 4{r} to the power of 3 square root of 2r - 5rsquare root of 13r + {r} to the power of 2 square root of 26r
e A LaTex expression showing 12{r} to the power of 2 square root of r + 4{r} to the power of 3 square root of 2r - 3rsquare root of 13r - {r} to the power of 2
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3square root of p + square root of 2) times (psquare root of 2p + 5)
a A LaTex expression showing {p} to the power of 2 square root of 2 - 15square root of p + 2psquare root of p + square root of 2
b A LaTex expression showing 3{p} to the power of 2 square root of 2 + 15square root of p + 2psquare root of p + 5square root of 2
c A LaTex expression showing 3psquare root of 2 + 15square root of 3p + 2psquare root of p + 5square root of 2
d A LaTex expression showing 3{p} to the power of 2 square root of 2 + 17psquare root of p + square root of 2
e A LaTex expression showing 3psquare root of 2p - 15square root of p + 6psquare root of p + 5square root of 2
6
A LaTex expression showing (5square root of x + {x} to the power of 2 square root of 13) times (xsquare root of 5x + 3xsquare root of x)
Multiply the radical expressions and simplify the answer
a A LaTex expression showing {x} to the power of 2 square root of 5 + {x} to the power of 4 square root of 65x - 15{x} to the power of 2 + 3{x} to the power of 3 square root of 13x
b A LaTex expression showing 5{x} to the power of 2 square root of 5 + {x} to the power of 3 square root of 65x + 15{x} to the power of 2 + 3{x} to the power of 3 square root of 13x
c A LaTex expression showing 5xsquare root of 5 + {x} to the power of 3 square root of 65x + 15{x} to the power of 2 - 3xsquare root of 13x
d A LaTex expression showing 5{x} to the power of 2 square root of 5 + {x} to the power of 3 square root of 65{x to the power of -1 } + 15{x} to the power of 3 - 3{x} to the power of 3 square root of 13x
e A LaTex expression showing 5{x} to the power of 2 square root of 5 + {x} to the power of 3 square root of x + 15{x} to the power of 2 - {x} to the power of 3 square root of 13x
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing (4c + square root of 13c) times (square root of 7c + 3csquare root of c)
a A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 2 square root of c + square root of 91 + 3csquare root of 13
b A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 3 square root of c + csquare root of 91 + 3csquare root of 13
c A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 2 square root of c + csquare root of 91 + 4{c} to the power of 4 square root of 13
d A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 2 square root of c + csquare root of 91 + 3{c} to the power of 2 square root of 13
e A LaTex expression showing 4csquare root of 7c + 12{c} to the power of 2 square root of c + square root of 91c - 3{c} to the power of 3 square root of 13
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing (3{b} to the power of 2 - {b} to the power of 2 square root of 7) times (bsquare root of 2b - 4{b} to the power of 2 )
a A LaTex expression showing 3{b} to the power of 3 square root of 2 - {b} to the power of 3 square root of 14b - 12{b} to the power of 4 + 4{b} to the power of 2 square root of 7
b A LaTex expression showing 3{b} to the power of 3 square root of 2b - {b} to the power of 3 square root of 14b - 12b + 4{b} to the power of 4 square root of 7
c A LaTex expression showing 3{b} to the power of 3 square root of 2b - {b} to the power of 3 square root of 14b - 12{b} to the power of 4 + 4{b} to the power of 4 square root of 7
d A LaTex expression showing 3{b} to the power of 3 square root of 2b - bsquare root of 14b + 12{b} to the power of 4 + 4{b} to the power of 5 square root of 7
e A LaTex expression showing 3{b} to the power of 3 square root of 2b - {b} to the power of 3 square root of b - 12{b} to the power of 4 + 4{b} to the power of 5 square root of 7