Solve 24c^{2}d^{2}e^{2}+84c^2d^2e-96cd^2e^3

$$24 c ^ { 2 } d ^ { 2 } e ^ { 2 } + 84 c ^ { 2 } d ^ { 2 } e - 96 c d ^ { 2 } e ^ { 3 }$$

Factor

$$12ec\left(2ec+7c-8e^{2}\right)d^{2}$$

Solution Steps

Factor out 12.

$$12\left(2c^{2}d^{2}e^{2}+7c^{2}d^{2}e-8cd^{2}e^{3}\right)$$

Consider 2c^{2}d^{2}e^{2}+7c^{2}d^{2}e-8cd^{2}e^{3}. Factor out cd^{2}e.

$$cd^{2}e\left(2ce+7c-8e^{2}\right)$$

Rewrite the complete factored expression.

$$12cd^{2}e\left(2ce+7c-8e^{2}\right)$$

Evaluate

$$12ec\left(2ec+7c-8e^{2}\right)d^{2}$$