Solve (a+3)(a-4)-(a-1)^2

$$( a + 3 ) ( a - 4 ) - ( a - 1 ) ^ { 2 }$$

Evaluate

$$a-13$$

Solution Steps

Use the distributive property to multiply a+3 by a-4 and combine like terms.

$$a^{2}-a-12-\left(a-1\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$a^{2}-a-12-\left(a^{2}-2a+1\right)$$

To find the opposite of a^{2}-2a+1, find the opposite of each term.

$$a^{2}-a-12-a^{2}+2a-1$$

Combine a^{2} and -a^{2} to get 0.

$$-a-12+2a-1$$

Combine -a and 2a to get a.

$$a-12-1$$

Subtract 1 from -12 to get -13.

$$a-13$$

Expand

$$a-13$$

Solution Steps

Use the distributive property to multiply a+3 by a-4 and combine like terms.

$$a^{2}-a-12-\left(a-1\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$a^{2}-a-12-\left(a^{2}-2a+1\right)$$

To find the opposite of a^{2}-2a+1, find the opposite of each term.

$$a^{2}-a-12-a^{2}+2a-1$$

Combine a^{2} and -a^{2} to get 0.

$$-a-12+2a-1$$

Combine -a and 2a to get a.

$$a-12-1$$

Subtract 1 from -12 to get -13.

$$a-13$$