Question

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

Answer 1

Answer:

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

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

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.

Answer 2

Step-by-step explanation:

25

2

−(x

2

−36)

=(5x)

2

−(x

2

−36)

2

By using identity a^2 – b^2

\begin{gathered}(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)\end{gathered}

(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.