Solve 32xy^2-50x+48zy^2-75z

$$32x { y }^{ 2 } -50x+48z { y }^{ 2 } -75z$$

Factor

$$\left(4y-5\right)\left(4y+5\right)\left(2x+3z\right)$$

Solution Steps

Do the grouping 32xy^{2}-50x+48zy^{2}-75z=\left(32xy^{2}-50x\right)+\left(48zy^{2}-75z\right), and factor out 2x in the first and 3z in the second group.

$$2x\left(16y^{2}-25\right)+3z\left(16y^{2}-25\right)$$

Factor out common term 16y^{2}-25 by using distributive property.

$$\left(16y^{2}-25\right)\left(2x+3z\right)$$

Consider 16y^{2}-25. Rewrite 16y^{2}-25 as \left(4y\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4y-5\right)\left(4y+5\right)$$

Rewrite the complete factored expression.

$$\left(4y-5\right)\left(4y+5\right)\left(2x+3z\right)$$

Evaluate

$$\left(2x+3z\right)\left(16y^{2}-25\right)$$