Question

Factor each of the following expressions. What similarities do you notice between the examples in the left column and those on the right? (a) x² − 1 (b) 9x² − 1 (c) x²+8x +15 (d) 4x²+16x +15 (e) x² − y² (f) x⁴ − y⁴

Answer 1

(a) (x+1)(x-1)

(b)(3x+1)(3x-1)

(c) (x+3)(x+5)

(d)(2x+5)(2x+3)

(e)(x+y)(x-y)

(f)
`(x^(2)  +y^(2))(x+y)(x-y)`

Explanation:

We have to factorize the following expressions:

(a) x²-1 =(x+1)(x-1) (Answer) {Since we know the formula (a²-b²) =(a+b)(a-b)}

(b) 9x²-1 =(3x+1)(3x-1) (Answer) {Since we know the formula (a²-b²) =(a+b)(a-b)}

(c) x²+8x+15 = x² +3x+5x+15 =(x+3)(x+5) (Answer)

(d) 4x²+16x+15 =4x²+10x+6x+15 = 2x(2x+5) +3(2x+5) =(2x+5)(2x+3) (Answer)

(e) x²-y² =(x+y)(x-y) (Answer)

(f)
`x^(4)-y^(4) =(x^(2)   +y^(2))(x^(2)  -y^(2))=(x^(2)  +y^(2))(x+y)(x-y)` (Answer) {Since we know the formula (a²-b²) =(a+b)(a-b)}