Solve 3x^2y^2-12x^2

$$3 x ^ { 2 } y ^ { 2 } - 12 x ^ { 2 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(x^{2}y^{2}-4x^{2}\right)$$

Consider x^{2}y^{2}-4x^{2}. Factor out x^{2}.

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

Consider y^{2}-4. Rewrite y^{2}-4 as y^{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).

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

Rewrite the complete factored expression.

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

Evaluate

$$3x^{2}\left(y^{2}-4\right)$$