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

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

Step-by-step explanation:

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

Step-by-step 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

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