Question

Factorise- 16x^2-24yz-gy^2-16z^2

Answer 1

SOLUTION;__®️

16x^2 -24yz-9y^2-16z^2 = (4x)^2 -24yz-(3y)^2-(4z)^2

    = -{(3y)^2+24yz+4z^2} + 4x^2

    = -(3y+4z)^2 + 4x^2    [using a^2+2ab+b^2 = (a+b)^2]

       = (4x)^2 -(3y+4z)^2

       = (4x+3y+4z) (4x-3y-4z)  [using a^2 - b^2 = (a+b)(a-b) where a=4x  &   b=3y+4z]

Answer 2

16x^2 -24yz-9y^2-16z^2 = (4x)^2 -24yz-(3y)^2-(4z)^2

            = -{(3y)^2+24yz+4z^2} + 4x^2

            = -(3y+4z)^2 + 4x^2    [using a^2+2ab+b^2 = (a+b)^2]

              = (4x)^2 -(3y+4z)^2

              = (4x+3y+4z) (4x-3y-4z)  [using a^2 - b^2 = (a+b)(a-b) where a=4x  &   b=3y+4z]