Solve 1/2a^2+2a-1+1/2a^2-2a

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

Evaluate

$$a^{2}-1$$

Solution Steps

Combine \frac{1}{2}a^{2} and \frac{1}{2}a^{2} to get a^{2}.

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

Combine 2a and -2a to get 0.

$$a^{2}-1$$

Factor

$$\left(a-1\right)\left(a+1\right)$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{a^{2}+4a-2+a^{2}-4a}{2}$$

Consider a^{2}+4a-2+a^{2}-4a. Multiply and combine like terms.

$$2a^{2}-2$$

Consider 2a^{2}-2. Factor out 2.

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

Consider a^{2}-1. Rewrite a^{2}-1 as a^{2}-1^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(a-1\right)\left(a+1\right)$$