Solve 16(a-3b)^2-4(a-3b)

$$16 ( a - 3 b ) ^ { 2 } - 4 ( a - 3 b )$$

Evaluate

$$4\left(a-3b\right)\left(4a-12b-1\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-3b\right)^{2}.

$$16\left(a^{2}-6ab+9b^{2}\right)-4\left(a-3b\right)$$

Use the distributive property to multiply 16 by a^{2}-6ab+9b^{2}.

$$16a^{2}-96ab+144b^{2}-4\left(a-3b\right)$$

Use the distributive property to multiply -4 by a-3b.

$$16a^{2}-96ab+144b^{2}-4a+12b$$

Expand

$$16a^{2}-96ab-4a+144b^{2}+12b$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-3b\right)^{2}.

$$16\left(a^{2}-6ab+9b^{2}\right)-4\left(a-3b\right)$$

Use the distributive property to multiply 16 by a^{2}-6ab+9b^{2}.

$$16a^{2}-96ab+144b^{2}-4\left(a-3b\right)$$

Use the distributive property to multiply -4 by a-3b.

$$16a^{2}-96ab+144b^{2}-4a+12b$$