Multiplication of Polynomial by monomial

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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 . a ³ b) + (-3ab . a ² b ² ) + ( -3ab . -ab)

= -3a ¹⁺³ b ¹⁺¹ - 3a ¹⁺² b ¹⁺² + 3a ¹⁺¹ b ¹⁺¹

= -3a ⁴ b ² - 3a ³ b ³ + 3a ² b ²

2) 3( 5 - 2d - d²)

Solution :

= (3 x 5) - (3 x 2d ) - (3 x d ² )

= 15 - 6d - 3d ²

3) -5a ( a³ - 2a² + 7a + 8)

Solution :

= ( -5a x a ³ ) + ( -5a x 2a ² ) + ( -5a x 7a) + (-5a x 8)

= -5a ⁴ - 10a ³ - 35a ² - 40a

4) 0(x⁴ + x³ + x² + x + 1)

Solution :

Any polynomial multiply by zero is zero.

So, 0 . (x ⁴ + x ³ + x ² + x + 1) = 0

5) 1 ( x⁴ - 7 )

Solution :

Any polynomial multiply by 1 is the polynomial itself.
So, 1 . ( x ⁴ - 7 ) = ( x ⁴ - 7 )

6) 2a/3(a ³ + 6a ² + 12)

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

= 2a ⁴ /3 + 4a ² + 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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