Solve 3a^{2}m^{2}p^{2}q^{3}-2am^{2}p^{2}q^{3}c-6ab^{2}cm^2+4b^2c^2m^2

$$3 a ^ { 2 } m ^ { 2 } p ^ { 2 } q ^ { 3 } - 2 a m ^ { 2 } p ^ { 2 } q ^ { 3 } c - 6 a b ^ { 2 } c m ^ { 2 } + 4 b ^ { 2 } c ^ { 2 } m ^ { 2 }$$

Factor

$$\left(3a-2c\right)m^{2}\left(ap^{2}q^{3}-2cb^{2}\right)$$

Solution Steps

Factor out m^{2}.

$$m^{2}\left(3a^{2}p^{2}q^{3}-2ap^{2}q^{3}c-6ab^{2}c+4b^{2}c^{2}\right)$$

Consider 3a^{2}p^{2}q^{3}-2ap^{2}q^{3}c-6ab^{2}c+4b^{2}c^{2}. Do the grouping 3a^{2}p^{2}q^{3}-2ap^{2}q^{3}c-6ab^{2}c+4b^{2}c^{2}=\left(3a^{2}p^{2}q^{3}-2ap^{2}q^{3}c\right)+\left(-6ab^{2}c+4b^{2}c^{2}\right), and factor out ap^{2}q^{3} in the first and -2cb^{2} in the second group.

$$ap^{2}q^{3}\left(3a-2c\right)-2cb^{2}\left(3a-2c\right)$$

Factor out common term 3a-2c by using distributive property.

$$\left(3a-2c\right)\left(ap^{2}q^{3}-2cb^{2}\right)$$

Rewrite the complete factored expression.

$$m^{2}\left(3a-2c\right)\left(ap^{2}q^{3}-2cb^{2}\right)$$

Evaluate

$$\left(3a-2c\right)m^{2}\left(ap^{2}q^{3}-2cb^{2}\right)$$