Solve 8(3a-2b)^2-10(3a-2b)

$$8 ( 3 a - 2 b ) ^ { 2 } - 10 ( 3 a - 2 b )$$

Evaluate

$$2\left(3a-2b\right)\left(12a-8b-5\right)$$

Solution Steps

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

$$8\left(9a^{2}-12ab+4b^{2}\right)-10\left(3a-2b\right)$$

Use the distributive property to multiply 8 by 9a^{2}-12ab+4b^{2}.

$$72a^{2}-96ab+32b^{2}-10\left(3a-2b\right)$$

Use the distributive property to multiply -10 by 3a-2b.

$$72a^{2}-96ab+32b^{2}-30a+20b$$

Expand

$$72a^{2}-96ab-30a+32b^{2}+20b$$

Solution Steps

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

$$8\left(9a^{2}-12ab+4b^{2}\right)-10\left(3a-2b\right)$$

Use the distributive property to multiply 8 by 9a^{2}-12ab+4b^{2}.

$$72a^{2}-96ab+32b^{2}-10\left(3a-2b\right)$$

Use the distributive property to multiply -10 by 3a-2b.

$$72a^{2}-96ab+32b^{2}-30a+20b$$