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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 ( a
3
b + a
2
b
2
- 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 - d
2
)
Solution :
= (3 x 5) - (3 x 2d ) - (3 x d
2
)
= 15 - 6d - 3d
2
3) -5a ( a
3
- 2a
2
+ 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(x
4
+ x
3
+ x
2
+ x + 1)
Solution :
Any polynomial multiply by zero is zero.
So, 0
.
(x
4
+ x
3
+ x
2
+ x + 1) = 0
5) 1 ( x
4
- 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
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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