Question

factories the following
1. 9x²-y²-16
2. a⁴+2ab+b⁴
3. 63a²-112b²


​

Answer 1

Factors:

In a

product of two or more expressions each expression is called a factor of the product.

Factorization:

The process

of writing a given expression as a product of two or more factors is called factorization.

Factorization when an expression is a complete square:

In this

case we use the following formula

1.

a²+2ab+b²= (a+b)²

2. a²-2ab+b²= (a-b)²

solution:

1) a² + 8a + 16 = a² + 2×a× 4 + 4²

[(a+b)²= a² +b² +2 ab]

=(a+4)²

2) p² - 10 p +25

= p²- 2xpx 5 + 5²

(a-b)²= a² +b² -2 ab =(p-5)²

3) 25m² + 30m + 9

= (5m)² + 2×5mx 3 + 3²

[(a+b)²= a² +b² +2ab] =(5m+3)²

4) 49y² + 84yz + 36z²

= (7y)² + 2x7yx 6z + (6z)²

[(a+b)²= a² +b² +2 ab ]

=(7y+6z)²

5) 4x² - 8x + 4

= (2x)² - 2×2×× 2 + 2²

[(a-b)²= a² +b² -2 ab] =(2x-2)²

= [2(x-1)² ] = 4(x-1) ²

6) 121b²-88bc + 16c²

= (11b)² - 2×11b× 4c + (4c)²

[(a-b)²= a² +b² -2 ab] =(11b-4c)²

7) (1 + m) 2 - 4lm

= 1² + m² +2lm -4lm

= 1² + m² -21m

[a-b)²= a² +b² -2ab] =(1-m)²

8) a² + 2a²b²+b4

= (a²)² + 2a²b²+(b²)²

[(a+b)²= a² +b² +2 ab ]

=(a²+b²)²

Hope this help you...