Question

Evaluate the expression $8x^3+125y^3$.

Answer 1

Evaluating the given expression:

The given expression is $8x^3+125y^3$.

It can be rewritten as $8x^3+125y^3={\left(2x\right)}^3+{\left(5y\right)}^3$.

We know that $a^3+b^3=(a+b)\left(a^2-ab+b^2\right)$.

Comparing expression with the identity we get, $a=2x,b=5y$.

Substitute values in identity we have:

$$\begin{gathered} {\left(2x\right)}^3+{\left(5y\right)}^3=\left(2x+5y\right)\left[{\left(2x\right)}^2-\left(2x\right)\left(5y\right)+{\left(5y\right)}^2\right] \\ =\left(2x+5y\right)\left(4x^2-10xy+25y^2\right) \end{gathered}$$

Hence, the expression, $8x^3+125y^3=\left(2x+5y\right)\left(4x^2-10xy+25y^2\right)$