Solve (x-1)^2+(x+2)(x-2)

$$( x - 1 ) ^ { 2 } + ( x + 2 ) ( x - 2 )$$

Evaluate

$$\left(x-1\right)^{2}+x^{2}-4$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

$$x^{2}-2x+1+x^{2}-4$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-2x+1-4$$

Subtract 4 from 1 to get -3.

$$2x^{2}-2x-3$$

Expand

$$2x^{2}-2x-3$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

$$x^{2}-2x+1+x^{2}-4$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-2x+1-4$$

Subtract 4 from 1 to get -3.

$$2x^{2}-2x-3$$