Solve 7r^5-56r^2g^3

$$7 r ^ { 5 } - 56 r ^ { 2 } g ^ { 3 }$$

Factor

$$7\left(r-2g\right)r^{2}\left(r^{2}+2gr+4g^{2}\right)$$

Solution Steps

Factor out 7.

$$7\left(r^{5}-8r^{2}g^{3}\right)$$

Consider r^{5}-8r^{2}g^{3}. Factor out r^{2}.

$$r^{2}\left(r^{3}-8g^{3}\right)$$

Consider r^{3}-8g^{3}. Rewrite r^{3}-8g^{3} as r^{3}-\left(2g\right)^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(r-2g\right)\left(r^{2}+2gr+4g^{2}\right)$$

Rewrite the complete factored expression.

$$7r^{2}\left(r-2g\right)\left(r^{2}+2gr+4g^{2}\right)$$

Evaluate

$$7r^{2}\left(r^{3}-8g^{3}\right)$$