Question

(x²+42x+49)²-y².
factorize

Answer 1

You could take (x square +42x +49)square as "A" and y square as "B"

Then it would fall in the formula A square - B square,which is (A+B)(A-B).

Otherwise you could try splitting the middle term of "A"

Answer 2

(9x^2 + 42x + 49)^2 - y^2

let 9x^2 + 42x + 49 be 'x'

9x^2 + 42x + 49

(3x)^2 + 2×3x×7 + (7)^2

it's in the form of a^2 +2ab+ b^2 = (a+b)^2

so (3x)^2 + 2×3x×7 + (7)^2 = (3x + 7)^2

so 'x' = (3x + 7)^2

( (3x + 7)^2)^2 - y^2

it's in the form of a^2 - b^2 = (a+b)(a-b)

So ( (3x + 7)^2)^2 - y^2

= (3x+y+7)(3x-y+7)