Solve x^3y^2-5x^2-4xy^2+20

$$x ^ { 3 } y ^ { 2 } - 5 x ^ { 2 } - 4 x y ^ { 2 } + 20$$

Factor

$$\left(x-2\right)\left(x+2\right)\left(xy^{2}-5\right)$$

Solution Steps

Do the grouping x^{3}y^{2}-5x^{2}-4xy^{2}+20=\left(x^{3}y^{2}-5x^{2}\right)+\left(-4xy^{2}+20\right), and factor out x^{2} in the first and -4 in the second group.

$$x^{2}\left(xy^{2}-5\right)-4\left(xy^{2}-5\right)$$

Factor out common term xy^{2}-5 by using distributive property.

$$\left(xy^{2}-5\right)\left(x^{2}-4\right)$$

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

$$\left(x-2\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$\left(xy^{2}-5\right)\left(x-2\right)\left(x+2\right)$$

Evaluate

$$\left(x^{2}-4\right)\left(xy^{2}-5\right)$$