Page 49 - SM inner class 8.cdr

2
Note: The dot con sid ered as mul ti pli ca tion if it ex ists Example 10. -3ab a b( 3 + a b 2 - ab)
be tween two terms. Solution:
3
2
(
= -3ab .a b ) + -3ab .a b 2 ) + -3ab ab )
- .
(
(
Step 2: Multiply the like variables.
b
= -3a 1 + 3 b 1 + 1 -3a 1 + 2 1 + 2 + 3a 1 + 1 b + 1 1
Step 3: Multiply the two partial products 4 2 3 3 2 2
= -3a b - 3a b + 3a b
obtained in step 1 and 2.
Example 11. -5a a( 3 - 2a 2 + 7a + 8)
2
5
Example 6. Find the product of p and p
Solution:
5
2
Solution: p ´ p = p 2 + 5 = p 7 3 2
= -5a ´ a ) + -5a ´ 2a ) + -5a ´ 7a )
(
(
(
2
Example 7. Find the product of 3ab and 4a b + -5a ´ )
(
8
2
Solution: 3ab ´ 4a b = -5a 4 -10a 3 - 35a 2 - 40a
2
4
= (3 ´ ) ´ a ´ a b ´ b
4. Multiplication of Polynomial by Binomial
1
+ 2
+ 1
3
1
2
=12a b =12a b
Multiplication of Polynomial by
2. Multiplication of Monomial by Binomial
Binomial, use the following steps :
For multiplication of monomial by
Step 1: Multiply every term of one
binomial use the following steps:
binomial by every term of the
1. Monomial is outside the parenthesis polynomial.
(bracket).
Step 2: Add the products and combine like
2. Binomial is inside the parenthesis. terms.
3. Use a distributive property to open the Example 12. (a + ab + b 2 ) (a - ) b
2
parenthesis. 2 2
Solution: (a + ab + b ) (a - ) b
4. Distributive property ® Multiply each Use a distributive property.
term of the parenthesis by the monomial 2 2
= a ( a - b) + ab a - b) + b ( a - b)
(
keeping the addition or subtraction sign 2 2 2 2
= a a - a b + ab a - ab b + b . a - b b
.
.
.
.
.
same. 3 2 2 2 2 3
= a - a b + a b - ab + ab - b
Example 8. Multiply : 3x x( + 4) [Add like terms]
Solution: As 3x is outside the parenthesis, and = a 3 - b 3
(x + 4 ) is inside the parenthesis so multiply x Example 13. (1 4- x ) (1 + x + x 2 )
and 4 by 3x
Solution: (1 4- x ) (1+ x + x 2 )
.
3x x + 4) = 3x x + 3 4
x
.
(
(
=1 1 + x + x 2 ) - 4 ( 1 + x + x 2 )
x
= 3x 1 + 1 + 12x
1
-
x
x
.
x
= + 1.x + 1.x 2 - 4 1 4 .x - 4 .x 2
2
= 3x + 12x
1
= + x + x 2 - 4x - 4x 2 - 4x 3
2
2
3
2
Example 9. Multiply : 4x y ( 3x y - 2xy)
[Bring the like terms together]
2
2
3
2
Solution: 4x y ( 3x y - 2xy) 2 2 3
= + x - 4x + x - 4x - 4x
1
2
2
2
3
= 4x y 3 × 3x y 2 - 4x y ×2xy
3
= -3x - 3x 2 - 4x [Add like terms]
1
3
4
=12x y 5 - 8x y 4 3 2
= -4x - 3x - 3x + 1
3. Multiplication of Polynomial by [arranging in descending
Monomial order of exponents]
For multiplication of polynomial by Example 14. (a - b 2 ) ( a - b 3 )
2
3
4
monomial, use the following steps : 2 2 3 3
Solution: (a - b ) ( a - b )
4
2
3
3
2
Step 1: Use a distributive law to multiply = a ( 4 a 3 - b ) - b ( 4 a 3 - b )
2 3
3
polynomial by monomial. = 4a 5 - a b - 4a b 2 + b 5
Step 2: Multiply each term of the
parenthesis by monomial.
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Mathematics In Focus - 8