Solve 15(a-3b)^2-10(a-3b)

$$15 ( a - 3 b ) ^ { 2 } - 10 ( a - 3 b )$$

Evaluate

$$5\left(a-3b\right)\left(3a-9b-2\right)$$

Solution Steps

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

$$15\left(a^{2}-6ab+9b^{2}\right)-10\left(a-3b\right)$$

Use the distributive property to multiply 15 by a^{2}-6ab+9b^{2}.

$$15a^{2}-90ab+135b^{2}-10\left(a-3b\right)$$

Use the distributive property to multiply -10 by a-3b.

$$15a^{2}-90ab+135b^{2}-10a+30b$$

Expand

$$15a^{2}-90ab-10a+135b^{2}+30b$$

Solution Steps

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

$$15\left(a^{2}-6ab+9b^{2}\right)-10\left(a-3b\right)$$

Use the distributive property to multiply 15 by a^{2}-6ab+9b^{2}.

$$15a^{2}-90ab+135b^{2}-10\left(a-3b\right)$$

Use the distributive property to multiply -10 by a-3b.

$$15a^{2}-90ab+135b^{2}-10a+30b$$