Multiplication of Polynomial by monomial

Multiplication of Polynomial by Monomial, use the following steps :

1) Use a distributive law to multiply polynomial by monomial.
2) Multiply each term of the parenthesis by monomial.


Some more examples :

1) -3ab ( a³b + a²b² - ab)

Solution :

= (-3ab. a³b) + (-3ab . a²b²) + ( -3ab . -ab)

= -3a¹⁺³b¹⁺¹ - 3a¹⁺²b¹⁺² + 3a¹⁺¹b¹⁺¹

= -3a⁴b² - 3a³b³ + 3a²b²

2) 3( 5 - 2d - d²)

Solution :

= (3 x 5) - (3 x 2d ) - (3 x d²)

= 15 - 6d - 3d²

3) -5a ( a³ - 2a² + 7a + 8)

Solution :

= ( -5a x a³) + ( -5a x 2a²) + ( -5a x 7a) + (-5a x 8)

= -5a⁴ - 10a³ - 35a² - 40a

4) 0(x⁴ + x³ + x² + x + 1)

Solution :

Any polynomial multiply by zero is zero.

So, 0.(x⁴ + x³ + x² + x + 1) = 0

5) 1 ( x⁴ - 7 )

Solution :

Any polynomial multiply by 1 is the polynomial itself.
So, 1.( x⁴ - 7 ) = ( x⁴ - 7 )

6) 2a/3(a³+ 6a² + 12)

Solution :
= ( 2a/3 x a³) + ( 2a/3 x 6a²) + ( 2a/3 x 12)

= 2a⁴/3 + 4a² + 8a

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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

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