Question

Factorise : $125a^3+\frac{1}{8}$

Answer 1

Given : $125a^3+\frac{1}{8}$

According to equation,

$a^3+b^3=(a+b)(a^2-ab+b^2)$

So we get,

$125a^3+\frac{1}{8}$$={\left(5a\right)}^3+{\frac{1}{2}}^3$

On the basis of formula,

$=(5a+\frac{1}{2})({\left(5a\right)}^2-\left(5a\right)\left(\frac{1}{2}\right){\left(\frac{1}{2}\right)}^2)$

$125a^3+\frac{1}{8}$$=(5a+\frac{1}{2})(25a^2-\frac{5}{2}a+\frac{1}{4})$