Question

Factorize (x^4-8x^2y^2+16y^4)-289​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{(x^4-8x^2y^2+16y^4)-289}$

$\underline{\textbf{To find:}}$

$\mathsf{Factors\;of\;(x^4-8x^2y^2+16y^4)-289}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{(x^4-8x^2y^2+16y^4)-289}$

$\textsf{This can be written as}$

$\mathsf{=[(x^2)^2-2(x^2)(4y^2)+(4y^2)^2]-289}$

$\textsf{Using the identity,}$

$\boxed{\mathsf{(a-b)^2=a^2-2ab+b^2}}$

$\mathsf{=(x^2-4y^2)^2-(17)^2}$

$\textsf{Using the identity,}$

$\boxed {\mathsf{a^2-b^2=(a-b)(a+b)}}$

$\mathsf{=(x^2-4y^2-17)(x^2-4y^2+17)}$

$\implies\boxed{\mathsf{(x^4-8x^2y^2+16y^4)-289=(x^2-4y^2-17)(x^2-4y^2+17)}}$

$\underline{\textbf{Find more:}}$

1.x^2-(a-1/a)x+1 factorise the following

https://brainly.in/question/4301404

2.Factorise x^4-(x-z)^4​

https://brainly.in/question/14993176

Answer 2

Step-by-step explanation: