Question

find continued product of (x+y) (x-y) (
`x^(2)`+
`y^(2)`) (
`x^(4)`+
`y^(4)`)

Answer 1

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

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`