Solve y=(x+2)(x-2)-(x-1)^2 | Microsoft Math Solver

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y=x^{2}-4-\left(x-1\right)^{2}

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.

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

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

y=x^{2}-4-x^{2}+2x-1

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

y=-4+2x-1

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

y=-5+2x

Subtract 1 from -4 to get -5.

-5+2x=y

Swap sides so that all variable terms are on the left hand side.

2x=y+5

Add 5 to both sides.

\frac{2x}{2}=\frac{y+5}{2}

Divide both sides by 2.

x=\frac{y+5}{2}

Dividing by 2 undoes the multiplication by 2.