This is the concept of polynomial function, the question requires us to compute;
(x+2y)^5
=(x+2y)^2(x+2y)^2(x+2y)
=[(x^2+4xy+4y^2)(x^2+4xy+4y^2)](x+2y)
=[x^2(x^2+4xy+4y^2)++4xy(x^2+4xy+4y^2)+4y^2(x^2+4xy+4y^2)](x+2y)
=(x^4+8x^3y+24x^2y^2+32xy^3+16y^4)(x+2y)
=x(x^4+8x^3y+24x^2y^2+32xy^3+16y^4)+2y(x^4+8x^3y+24x^2y^2+32xy^3+16y^4)
=x^5+10x^4y+40x^3y^2+80x^3y^3+80xy^4+32y^5
the answer is:
=x^5+10x^4y+40x^3y^2+80x^3y^3+80xy^4+32y^5
