Question

25^2 – (x^2 – 36)^2 Factorise it please.​

Answer 1

$\huge\underline\bold {Answer:}$

$25 {}^{2} - (x {}^{2} - 36) \\ = (5x) {}^{2} - ( {x}^{2} - 36) {}^{2}$

By using identity a^2 – b^2

$(5x + x {}^{2} - 36)(5x - x {}^{2} + 36) \\ = (x {}^{2} + 5x - 36) { - (x {}^{2} - 5x - 36)} \\ = ( {x}^{2} + 9x - 4x - 36){ - (x(x - 9) + 4(x - 9)} \\ = {x(x + 9) - 4(x + 9)}{ - (x(x - 9) + 4(x - 9)} \\ = (x + 9)(x - 4){ - x(x - 9)(x + 4)} \\ = (x + 9)(x - 4)(9 - x)(4 + x)$

Hence, (x + 9)(x – 4)(9– x)(4+x) is the answer.