Solve 7(a-2b)^2-25(a-2b)+12

$$7 ( a - 2 b ) ^ { 2 } - 25 ( a - 2 b ) + 12$$

Evaluate

$$\left(a-2b-3\right)\left(7a-14b-4\right)$$

Solution Steps

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

$$7\left(a^{2}-4ab+4b^{2}\right)-25\left(a-2b\right)+12$$

Use the distributive property to multiply 7 by a^{2}-4ab+4b^{2}.

$$7a^{2}-28ab+28b^{2}-25\left(a-2b\right)+12$$

Use the distributive property to multiply -25 by a-2b.

$$7a^{2}-28ab+28b^{2}-25a+50b+12$$

Expand

$$7a^{2}-28ab-25a+28b^{2}+50b+12$$

Solution Steps

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

$$7\left(a^{2}-4ab+4b^{2}\right)-25\left(a-2b\right)+12$$

Use the distributive property to multiply 7 by a^{2}-4ab+4b^{2}.

$$7a^{2}-28ab+28b^{2}-25\left(a-2b\right)+12$$

Use the distributive property to multiply -25 by a-2b.

$$7a^{2}-28ab+28b^{2}-25a+50b+12$$