Question

14(3y-5z)^3+7(3y-5z)^2

Answer 1

Given 14(3y - 5z)^3 + 7(3y - 5z)^2.      ------ (1)

We know that (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3.

                (3y - 5z)^3 = 3y^3 - 3(3y)^2 * 5z + 3(3y)(5z)^2 - (5z)^3

                                  = 27y^3 - 135y^2z + 225yz^2 - 125z^3.     ------ (2)


We know that (a-b)^2 = a^2 + b^2 - 2ab

              Then (3y - 5z)^2 = (3y)^2 + (5z)^2 - 2(3y)(5z)

                                          = 9y^2 + 25z^2 - 30yz   ---------------- (3)


Substitute (2) & (3) in (1) , we get

= 14(27y^3 - 135y^2z + 225yz^2 - 125z^3) + 7(9y^2 + 25z^2 - 30yz)

= 378y^3 - 1890y^2z + 3150yz^2 - 1750z^3 + 7(9y^2 + 25z^2 - 30yz)

= 378y^3 - 1890y^2z + 3150yz^2 - 1750z^3 + 63y^2 + 175z^2 - 210yz

= 378y^3 - 1890y^2z + 3150yz^2 - 1750z^3 - 210yz + 175z^2.



Hope this helps!