Solve 2(3a^2-1)-(a+2)(a+2)

$$2 ( 3 a ^ { 2 } - 1 ) - ( a + 2 ) ( a + 2 )$$

Evaluate

$$5a^{2}-4a-6$$

Solution Steps

Multiply a+2 and a+2 to get \left(a+2\right)^{2}.

$$2\left(3a^{2}-1\right)-\left(a+2\right)^{2}$$

Use the distributive property to multiply 2 by 3a^{2}-1.

$$6a^{2}-2-\left(a+2\right)^{2}$$

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

$$6a^{2}-2-\left(a^{2}+4a+4\right)$$

To find the opposite of a^{2}+4a+4, find the opposite of each term.

$$6a^{2}-2-a^{2}-4a-4$$

Combine 6a^{2} and -a^{2} to get 5a^{2}.

$$5a^{2}-2-4a-4$$

Subtract 4 from -2 to get -6.

$$5a^{2}-6-4a$$

Expand

$$5a^{2}-4a-6$$

Solution Steps

Multiply a+2 and a+2 to get \left(a+2\right)^{2}.

$$2\left(3a^{2}-1\right)-\left(a+2\right)^{2}$$

Use the distributive property to multiply 2 by 3a^{2}-1.

$$6a^{2}-2-\left(a+2\right)^{2}$$

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

$$6a^{2}-2-\left(a^{2}+4a+4\right)$$

To find the opposite of a^{2}+4a+4, find the opposite of each term.

$$6a^{2}-2-a^{2}-4a-4$$

Combine 6a^{2} and -a^{2} to get 5a^{2}.

$$5a^{2}-2-4a-4$$

Subtract 4 from -2 to get -6.

$$5a^{2}-6-4a$$