Solve ax^2-49ay^2=

$$a x ^ { 2 } - 49 a y ^ { 2 } =$$

Factor

$$a\left(x-7y\right)\left(x+7y\right)$$

Solution Steps

Factor out a.

$$a\left(x^{2}-49y^{2}\right)$$

Consider x^{2}-49y^{2}. Rewrite x^{2}-49y^{2} as x^{2}-\left(7y\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(x-7y\right)\left(x+7y\right)$$

Rewrite the complete factored expression.

$$a\left(x-7y\right)\left(x+7y\right)$$

Evaluate

$$a\left(x^{2}-49y^{2}\right)$$