Question

factorise the following by expressing as a difference of two square (x+y)^4-(x-y)^4​

Answer 1

Answer:

The factorization would be $8xy(x^2+y^2)$

Step-by-step explanation:

$(x+y)^4-(x-y)^4\\=[(x+y)^2]^2-[(x-y)^2]^2\\=[(x+y)^2+(x-y)^2][(x+y)^2-(x-y)^2]\\=(x^2+2xy+y^2+x^2-2xy+y^2)[(x+y)+(x-y)][(x+y)-(x-y)]\\=2*(x^2+y^2)(x+y+x-y) (x+y-x+y)\\=2*(x^2+y^2)*2x*2y\\=8xy(x^2+y^2)$