Solve (+28a^{5}b^{4}c-16a^{3}b^{3}c^2-4a^2b^2c^3):(-4c

$$( + 28 a ^ { 5 } b ^ { 4 } c - 16 a ^ { 3 } b ^ { 3 } c ^ { 2 } - 4 a ^ { 2 } b ^ { 2 } c ^ { 3 } ) : ( - 4 c$$

Factor

$$-\frac{4a^{2}b^{2}\left(7b^{2}a^{3}-4abc-c^{2}\right)}{4}$$

Solution Steps

Factor the expressions that are not already factored in \frac{28a^{5}b^{4}c-16a^{3}b^{3}c^{2}-4a^{2}b^{2}c^{3}}{-4c}.

$$factor(\frac{4ca^{2}b^{2}\left(-4abc+7b^{2}a^{3}-c^{2}\right)}{-4c})$$

Cancel out 4c in both numerator and denominator.

$$factor(\frac{a^{2}b^{2}\left(-4abc+7b^{2}a^{3}-c^{2}\right)}{-1})$$

Anything divided by -1 gives its opposite.

$$factor(-a^{2}b^{2}\left(-4abc+7b^{2}a^{3}-c^{2}\right))$$

Use the distributive property to multiply a^{2}b^{2} by -4abc+7b^{2}a^{3}-c^{2}.

$$factor(-\left(-4ca^{3}b^{3}+7a^{5}b^{4}-a^{2}b^{2}c^{2}\right))$$

To find the opposite of -4ca^{3}b^{3}+7a^{5}b^{4}-a^{2}b^{2}c^{2}, find the opposite of each term.

$$factor(4ca^{3}b^{3}-7a^{5}b^{4}+a^{2}b^{2}c^{2})$$

Factor out a^{2}b^{2}.

$$a^{2}b^{2}\left(4cab-7a^{3}b^{2}+c^{2}\right)$$

Evaluate

$$-\left(7b^{2}a^{3}-4abc-c^{2}\right)\left(ab\right)^{2}$$