Question

Factorise the expression 4(x+1)^2 -49 completely

Answer 1

(2x - 5)(2x + 9)

Explanation:

4(x + 1)² - 49 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

Thus

4(x + 1)² - 49

= (2(x + 1))² - 7² → a = 2(x + 1) and b = 7

= (2(x + 1) - 7)(2(x + 1) + 7)

= (2x + 2 - 7)(2x + 2 + 7)

= (2x - 5)(2x + 9) ← in factored form

Answer 2

(2x + 5)(2x - 9)

Explanation:

`4(x+1)^2 -49 \\ = \{2(x + 1) \} ^(2) - {(7)}^(2) \\ = (2x - 2)^(2) - {(7)}^(2) \\ = (2x - 2 + 7)(2x - 2 - 7) \\ = \red{ \boxed{ \bold{(2x + 5)(2x - 9)}}} \\`