Solve 4a^2c^2-16x^2y^2=

$$4 a ^ { 2 } c ^ { 2 } - 16 x ^ { 2 } y ^ { 2 } =$$

Factor

$$4\left(ac-2xy\right)\left(2xy+ac\right)$$

Solution Steps

Factor out 4.

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

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

$$\left(ac-2xy\right)\left(ac+2xy\right)$$

Reorder the terms.

$$\left(-2xy+ac\right)\left(2xy+ac\right)$$

Rewrite the complete factored expression.

$$4\left(-2xy+ac\right)\left(2xy+ac\right)$$

Evaluate

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