Solve 98a^2b^2-50x^2y^2=

$$98 a ^ { 2 } b ^ { 2 } - 50 x ^ { 2 } y ^ { 2 } =$$

Factor

$$2\left(7ab-5xy\right)\left(5xy+7ab\right)$$

Solution Steps

Factor out 2.

$$2\left(49a^{2}b^{2}-25x^{2}y^{2}\right)$$

Consider 49a^{2}b^{2}-25x^{2}y^{2}. Rewrite 49a^{2}b^{2}-25x^{2}y^{2} as \left(7ab\right)^{2}-\left(5xy\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(7ab-5xy\right)\left(7ab+5xy\right)$$

Reorder the terms.

$$\left(-5xy+7ab\right)\left(5xy+7ab\right)$$

Rewrite the complete factored expression.

$$2\left(-5xy+7ab\right)\left(5xy+7ab\right)$$

Evaluate

$$98\left(ab\right)^{2}-50\left(xy\right)^{2}$$