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

$$( a + 1 ) ( a - 1 ) - a ( a + 2 ) + 2$$

Evaluate

$$1-2a$$

Solution Steps

Consider \left(a+1\right)\left(a-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 1 to the power of 2 and get 1.

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

Use the distributive property to multiply a by a+2.

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

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

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

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

$$-1-2a+2$$

Add -1 and 2 to get 1.

$$1-2a$$

Expand

$$1-2a$$

Solution Steps

Consider \left(a+1\right)\left(a-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 1 to the power of 2 and get 1.

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

Use the distributive property to multiply a by a+2.

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

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

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

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

$$-1-2a+2$$

Add -1 and 2 to get 1.

$$1-2a$$