Question

Factorise each of the following: (x + 2)² – (x + 4)² using identites​

Answer 1

Answer:

-4(x+3)

Step-by-step explanation:

(x^2 + 4 + 4x) - (x^2 + 16 +8x)

= x^2 + 4 + 4x - x^2 - 16 - 8x

= -12 -4x

= -4(x+3)

Answer 2

To Factorise: (x + 2)² - (x + 4)²

We know,

a² - b² = (a + b)(a - b)

Similarly,

(x + 2)² - (x + 4)²

= [(x + 2) + (x + 4)] [(x + 2) - (x + 4)]

= (x + 2 + x + 4)(x + 2 - x - 4)

= (2x + 6)(-2)

= -2 (2x + 6)

∴ Factorised form of [(x + 2)² - (x + 4)²] is [-2 (2x + 6)].