Question

Question 92 (xxvii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$(x+y{)}^4-(x-y{)}^4$

Answer 1

$(x+y{)}^4-(x-y{)}^4=\left[\right(x+y{)}^2{]}^2-\left[\right(x-y{)}^2{]}^2=\left[\right(x+y{)}^2+(x-y{)}^2]\left[\right(x+y{)}^2-(x-y{)}^2]=(x^2+y^2+2xy+x^2+y^2-2xy)(x+y+x-y)(x+y-x+y)\left[Usingtheidentity\right(a+b{)}^2=a^2+2ab+b^2]=(2x^2+2y^2\left)\right(2x\left)\right(2y)=2(x^2+y^2\left)\right(2x\left)\right(2y)=8xy(x^2+y^2)$