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

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

Evaluate

$$\left(a+2b-4\right)\left(3a+6b+2\right)$$

Solution Steps

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

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

Use the distributive property to multiply 3 by a^{2}+4ab+4b^{2}.

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

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

$$3a^{2}+12ab+12b^{2}-10a-20b-8$$

Expand

$$3a^{2}+12ab-10a+12b^{2}-20b-8$$

Solution Steps

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

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

Use the distributive property to multiply 3 by a^{2}+4ab+4b^{2}.

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

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

$$3a^{2}+12ab+12b^{2}-10a-20b-8$$