Solve x^3-x^2y-49x+49y=

$$x ^ { 3 } - x ^ { 2 } y - 49 x + 49 y =$$

Factor

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

Solution Steps

Do the grouping x^{3}-x^{2}y-49x+49y=\left(x^{3}-x^{2}y\right)+\left(-49x+49y\right), and factor out x^{2} in the first and -49 in the second group.

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

Factor out common term x-y by using distributive property.

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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