Solve bc^2-4b+3c^2-12

$$b c ^ { 2 } - 4 b + 3 c ^ { 2 } - 12$$

Factor

$$\left(c-2\right)\left(b+3\right)\left(c+2\right)$$

Solution Steps

Do the grouping bc^{2}-4b+3c^{2}-12=\left(bc^{2}-4b\right)+\left(3c^{2}-12\right), and factor out b in the first and 3 in the second group.

$$b\left(c^{2}-4\right)+3\left(c^{2}-4\right)$$

Factor out common term c^{2}-4 by using distributive property.

$$\left(c^{2}-4\right)\left(b+3\right)$$

Consider c^{2}-4. Rewrite c^{2}-4 as c^{2}-2^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(c-2\right)\left(c+2\right)$$

Rewrite the complete factored expression.

$$\left(c-2\right)\left(c+2\right)\left(b+3\right)$$

Evaluate

$$\left(b+3\right)\left(c^{2}-4\right)$$