# Multiplication of Monomial by Binomial

In Multiplication of Monomial by Binomial,monomial means single number and Binomial has two terms.

For solving this multiplication use the following steps:

1) Monomial is outside the parenthesis (bracket).
2) Binomial is inside the parenthesis.
3) Use a distributive property to open the parenthesis.
4) Distributive property ---> Multiply each term of the parenthesis by the monomial keeping the addition or subtraction sign same.

Examples :

1) Multiply : 3x(x + 4)

Solution :
As 3x is outside the parenthesis, multiply x and 4 by 3x
3x(x + 4) = 3x
. x + 3x . 4
= 3x
1 + 1 + 12x
= 3x
2 + 12x

2) Multiply : 4x
2 y 3 (3x 2 y 2 - 2xy)

Solution :
4x
2 y 3 (3x 2 y 2 - 2xy)
= 4x
2 y 3 . 3x 2 y 2 - 4x 2 y 3 . 2xy
= 12x
4 y 5 - 8x 3 y 4

3) Multiply : -2xy (x
2 y - 4x)

Solution :
-2xy (x
2 y - 4x)
= -2xy
. x 2 + 2xy . 4x
= -2x
3 y 2 + 8x 2 y

4) Multiply : 3ab(a
2 b - ab 2 )

Solution :
3ab(a
2 b - ab 2 )
= 3ab
. a 2 b - 3ab . ab 2
= 3a
3 b 2 - 3a 2 b 3
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Practice

1) -4ab(2a
2 + 5ab)
2) 3x(4y
2 - x 3 )
3) -2(a
2 + 2b 2 )
4) 2/3(6x
2 + 9y)
5) -1/2(12x
2 - 18y 2 )

Multiplication of algebraic expressions

Multiplication of Monomial by Binomial
Multiplication of Binomial by Binomial
Multiplication of Polynomial by Monomial
Multiplication of Polynomial by Binomial

Algebraic Expressions page