Factorise $125{{x}^{3}}+27{{y}^{3}}$ completely. Hence simplify \(\frac{125{{x}^{3}}+27{{y}^{3}}}{

Question

Factorise $125{{x}^{3}}+27{{y}^{3}}$ completely. Hence simplify $\frac{125{{x}^{3}}+27{{y}^{3}}}{25{{x}^{2}}-15xy+9{{y}^{2}}}$. Assume $x,y$ are real and not both zero, so the denominator is nonzero.

Accepted Answer

$125x^3+27y^3=(5x+3y)(25x^2-15xy+9y^2)$. The fraction simplifies to $5x+3y$, for the stated nonzero denominator.

Polynomials, Cubic Equations and Partial Fractions - Factorisation by Special Identities

Polynomials, Cubic Equations and Partial Fractions - Factorisation by Special Identities

Video Solution:

Solution:

Solution locked