Solve x^{2}a^{2}-x^2b^2+4a^2-4b^2=

$$x ^ { 2 } a ^ { 2 } - x ^ { 2 } b ^ { 2 } + 4 a ^ { 2 } - 4 b ^ { 2 } =$$

Factor

$$\left(a-b\right)\left(a+b\right)\left(x^{2}+4\right)$$

Solution Steps

Do the grouping x^{2}a^{2}-x^{2}b^{2}+4a^{2}-4b^{2}=\left(x^{2}a^{2}-x^{2}b^{2}\right)+\left(4a^{2}-4b^{2}\right), and factor out x^{2} in the first and 4 in the second group.

$$x^{2}\left(a^{2}-b^{2}\right)+4\left(a^{2}-b^{2}\right)$$

Factor out common term a^{2}-b^{2} by using distributive property.

$$\left(a^{2}-b^{2}\right)\left(x^{2}+4\right)$$

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

$$\left(a-b\right)\left(a+b\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+4 is not factored since it does not have any rational roots.

$$\left(x^{2}+4\right)\left(a-b\right)\left(a+b\right)$$

Evaluate

$$\left(x^{2}+4\right)\left(a^{2}-b^{2}\right)$$