Question

find continued product of (x+y) (x-y) ( align="absmiddle" class="latex-formula">+$y^{2}$) ($x^{4}$+$y^{4}$)

Answer 1

Answer:

$\large\boxed{(x+y)(x-y)(x^2+y^2)(x^4+y^4)=x^8-y^8}$

Step-by-step explanation:

$(x+y)(x-y)(x^2+y^2)(x^4+y^4)\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\qquad(*)\\\\=\underbrace{(x+y)(x-y)}_{(*)}(x^2+y^2)(x^4+y^4)\\\\=\underbrace{(x^2-y^2)(x^2+y^2)}_{(*)}(x^4+y^4)\\\\=\left((x^2)^2-(y^2)^2\right)(x^4+y^4)\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\underbrace{(x^4-y^4)(x^4+y^4)}_{(*)}\\\\=\left(x^4\right)^2-\left(y^4\right)^2=x^8-y^8$