Question

C=3.(x\(^2\)-8y\(^3\)-15)-3.(x-2y).(x\(^2\)+2xy+4y\(^2\))

Answer 1

\(C=3.\left(x^2-8y^3-15\right)-3\left(x-2y\right)\left(x^2+2xy+4y^2\right)\)

\(=3x^2-24y^3-45-3\left[x\left(x^2+2xy+4y^2\right)-2y\left(x^2+2xy+4y^2\right)\right]\)

\(=3x^2-24y^3-45-3\left[\left(x^3+2x^2y+4xy^2\right)-\left(2x^2y+4xy^2+8y^3\right)\right]\)

\(=3x^2-24y^3-45-3\left(x^3+2x^2y+4xy^2-2x^2y-4xy^2-8y^3\right)\)

\(=3x^2-24y^3-45-3\left(x^3-8y^3\right)\)

\(=3x^2-24y^3-45-3x^3+24y^3\)

\(=3x^2-3x^3-45\)