a)
P=(5x−1)+2(1−5x)(4+5x)+(5x+4)2
P=(5x−1)2+2(1−5x)(4+5x)+(5x+4)2−(5x−1)2
P=(5x−1+5x+4)2−(5x−1)2
P=(5x−1+5x+4−5x+1)(5x−1+5x+4+5x−1
b)
Q= (x-y)^3 + (x+y)^3 + (y-x)^3 - [3xy(x+y)]
(x-y)^3 = x^3 - 3x^2y + 3xy^2 - y^3
(x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3
(y-x)^3 = y^3 - 3xy^2 + 3x^2y - x^3
Q= (2x^3 + 6xy^2) + (y^3 - 3xy^2 + 3x^2y - x^3) - [3xy(x+y)]
= (x^3 + 3xy^2 + 3x^2y + y^3) - 3x^2y - 3xy^2
Q= x^3 + y^3