Question

64x^3-27y^3+8z^3+72xyz

Answer 1

Given: The term 64x^3 - 27y^3 + 8z^3 + 72xyz

To find: Factorise it.

Solution:

• Now we have given the term as  64x^3 - 27y^3 + 8z^3 + 72xyz

• We can rewrite it as:

                  (4x)^3 + (-3y)^3 + (2z)^3 - 3(4x)(-3y)(2z)

• Now we know the formula:

                  a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)

• So applying it, we get:

                  (4x - 3y + 2z) ((4x)^2 + (-3y)^2 + (2z)^2 - (4x)(-3y) + (3y)(2z) - 2z)(4x))

                  (4x - 3y + 2z) (16x^2 + 9y^2 + 4z^2 + 12xy + 6yz - 8zx)

Answer:

            So the factors are:

            (4x - 3y + 2z) (16x^2 + 9y^2 + 4z^2 + 12xy + 6yz - 8zx)