Question

a) (ab)^3 - (a^2)^3=
b) (t^5)^3 - (2tz)^3=
c) (x^2y)^3 - (xy^2)^3=

Answer 1

formula a³-b³=(a-b)(a²+ab+b²)

a) (ab)^3 - (a^2)^3=(ab-a^2)(a^2b^2+a^3b+b^2)=a(b-a)(a^2b^2+a^3b+b^2)

b) (t^5)^3 - (2tz)^3=(t^5-2tz)(t^10+2t^6z+t^2z^2)=
=t(t^4-2z)(t^10+2t^6z+t^2z^2)

c) (x^2y)^3 - (xy^2)^3= (x^2y-xy^2)(x^4y^2+x^3y^3+x^2y^4)=
=xy(x-y)(x^4y^2+x^3y^3+x^2y^4)