Solve 7a^{3}b^{4}+14a^2b^2-21a^4b^2

$$7 a ^ { 3 } b ^ { 4 } + 14 a ^ { 2 } b ^ { 2 } - 21 a ^ { 4 } b ^ { 2 }$$

Factor

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

Solution Steps

Factor out 7.

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

Consider a^{3}b^{4}+2a^{2}b^{2}-3a^{4}b^{2}. Factor out a^{2}b^{2}.

$$a^{2}b^{2}\left(ab^{2}+2-3a^{2}\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$7\left(2+ab^{2}-3a^{2}\right)\left(ab\right)^{2}$$