Solve ax^4-9ay^2

$$a x ^ { 4 } - 9 a y ^ { 2 }$$

Factor

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

Solution Steps

Factor out a.

$$a\left(x^{4}-9y^{2}\right)$$

Consider x^{4}-9y^{2}. Rewrite x^{4}-9y^{2} as \left(x^{2}\right)^{2}-\left(3y\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Rewrite the complete factored expression.

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

Evaluate

$$a\left(x^{4}-9y^{2}\right)$$