Solve 20asqrt[3]{125b^7}-14sqrt[3]{216b^8}

$$20 a \sqrt[ 3 ] { 125 b ^ { 7 } } - 14 \sqrt[ 3 ] { 216 b ^ { 8 } }$$

Factor

$$4\left(25a-21\sqrt[3]{b}\right)b^{\frac{7}{3}}$$

Solution Steps

Factor out 2.

$$2\left(50ab^{\frac{7}{3}}-42b^{\frac{8}{3}}\right)$$

Consider 10a\sqrt[3]{125}b^{\frac{7}{3}}-7\sqrt[3]{216}b^{\frac{8}{3}}. Factor out b^{\frac{7}{3}}.

$$b^{\frac{7}{3}}\left(50a-42\sqrt[3]{b}\right)$$

Rewrite the complete factored expression.

$$2b^{\frac{7}{3}}\left(50a-42\sqrt[3]{b}\right)$$

Evaluate

$$100ab^{\frac{7}{3}}-84b^{\frac{8}{3}}$$