Solve 16a^2-9b^2+6b-1

$$16 a ^ { 2 } - 9 b ^ { 2 } + 6 b - 1$$

Factor

$$\left(4a+3b-1\right)\left(4a-3b+1\right)$$

Solution Steps

Rewrite as difference of two terms.

$$16a^{2}-\left(9b^{2}-6b+1\right)$$

Rewrite the terms as squares.

$$\left(4a\right)^{2}-\left(1-3b\right)^{2}$$

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

$$\left(4a-1+3b\right)\left(4a+1-3b\right)$$

Evaluate

$$-\left(3b-1\right)^{2}+16a^{2}$$