Simplify the following: $(2x - 5y)^{3} - (2x + 5y)^{3}$

Question

Aicharya · Accepted Answer

Given $(2x - 5y)^3 - (2x + 5y)^3$ We shall use the identity $a^3 - b^3 = (a - b)(a^2 + b^2 + ab)$ Here $a = (2x - 5y)$, $b = (2x + 5y)$ By applying the identity we get $= (2x - 5y - 2x + 5y) [(2x - 5y)^2 + (2x + 5y)^2 + (2x - 5y)(2x + 5y)]$ $= (2x - 5y - 2x - 5y) [(2x)^2 + (5y)^2 - 2(2x)(5y) + (2x)^2 + (5y)^2 + 2(2x)(5y) + (4x^2 - 25y^2)]$ $= (-10y) [(4x^2 + 25y^2 - 20xy) + (4x^2 + 25y^2 + 20xy) + 4x^2 - 25y^2]$ $= (-10y) [4x^2 + 25y^2 - 20xy + 4x^2 + 25y^2 + 20xy + 4x^2 - 25y^2]$ By rearranging the variable we get, $= (-10y) [4x^2 + 4x^2 + 4x^2 + 25y^2]$ $= -10y [12x^2 + 25y^2]$ $= -120x^2y - 250y^3$ Hence the value of $(2x - 5y)^3 - (2x + 5y)^3$ is $-120x^2y - 250y^3$.

Simplify the following: $(2x - 5y)^{3} - (2x + 5y)^{3}$

Solution