Solve (4)9x^2-a^2-2ab-b^2

$$( 4 ) 9 x ^ { 2 } - a ^ { 2 } - 2 a b - b ^ { 2 }$$

Factor

$$\left(6x-a-b\right)\left(6x+a+b\right)$$

Solution Steps

Multiply and combine like terms.

$$36x^{2}-2ab-a^{2}-b^{2}$$

Rewrite as difference of two terms.

$$36x^{2}-\left(2ab+a^{2}+b^{2}\right)$$

Rewrite the terms as squares.

$$\left(6x\right)^{2}-\left(a+b\right)^{2}$$

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

$$\left(6x-a-b\right)\left(6x+a+b\right)$$

Evaluate

$$-\left(a+b\right)^{2}+36x^{2}$$

Solution Steps

Multiply 4 and 9 to get 36.

$$36x^{2}-a^{2}-2ab-b^{2}$$