Solve 5left(3a+bright)^2+6left(3a+bright)-8

$$5 { \left(3a+b \right) }^{ 2 } +6 \left( 3a+b \right) -8$$

Evaluate

$$\left(15a+5b-4\right)\left(3a+b+2\right)$$

Solution Steps

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

$$5\left(9a^{2}+6ab+b^{2}\right)+6\left(3a+b\right)-8$$

Use the distributive property to multiply 5 by 9a^{2}+6ab+b^{2}.

$$45a^{2}+30ab+5b^{2}+6\left(3a+b\right)-8$$

Use the distributive property to multiply 6 by 3a+b.

$$45a^{2}+30ab+5b^{2}+18a+6b-8$$

Expand

$$45a^{2}+30ab+18a+5b^{2}+6b-8$$

Solution Steps

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

$$5\left(9a^{2}+6ab+b^{2}\right)+6\left(3a+b\right)-8$$

Use the distributive property to multiply 5 by 9a^{2}+6ab+b^{2}.

$$45a^{2}+30ab+5b^{2}+6\left(3a+b\right)-8$$

Use the distributive property to multiply 6 by 3a+b.

$$45a^{2}+30ab+5b^{2}+18a+6b-8$$