Solve Using the Quadratic Formula a^2-2ab+b^2

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

Set $a^{2} - 2 a b + b^{2}$ equal to $0$ .

$a^{2} - 2 a b + b^{2} = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = - 2 b$ , and $c = b^{2}$ into the quadratic formula and solve for $a$ .

$\frac{2 b \pm \sqrt{{(- 2 b)}^{2} - 4 \cdot (1 \cdot b^{2})}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Rewrite $4 \cdot 1 \cdot b^{2}$ as ${(2 \cdot 1 b)}^{2}$ .

$a = \frac{2 b \pm \sqrt{{(- 2 b)}^{2} - {(2 \cdot (1 b))}^{2}}}{2 \cdot 1}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = - 2 b$ and $b = 2 \cdot 1 b$ .

$a = \frac{2 b \pm \sqrt{(- 2 b + 2 \cdot (1 b)) (- 2 b - (2 \cdot (1 b)))}}{2 \cdot 1}$

Simplify.

Factor $2 b$ out of $- 2 b + 2 \cdot 1 b$ .

Factor $2 b$ out of $- 2 b$ .

$a = \frac{2 b \pm \sqrt{(2 b (- 1) + 2 \cdot (1 b)) (- 2 b - (2 \cdot (1 b)))}}{2 \cdot 1}$

Factor $2 b$ out of $2 \cdot 1 b$ .

$a = \frac{2 b \pm \sqrt{(2 b (- 1) + 2 b (1)) (- 2 b - (2 \cdot (1 b)))}}{2 \cdot 1}$

Factor $2 b$ out of $2 b (- 1) + 2 b (1)$ .

$a = \frac{2 b \pm \sqrt{2 b (- 1 + 1) (- 2 b - (2 \cdot (1 b)))}}{2 \cdot 1}$

Add $- 1$ and $1$ .

$a = \frac{2 b \pm \sqrt{2 b \cdot (0 (- 2 b - (2 \cdot (1 b))))}}{2 \cdot 1}$

Combine exponents.

Multiply $0$ by $2$ .

$a = \frac{2 b \pm \sqrt{0 b (- 2 b - (2 \cdot (1 b)))}}{2 \cdot 1}$

Multiply $0$ by $b$ .

$a = \frac{2 b \pm \sqrt{0 (- 2 b - (2 \cdot (1 b)))}}{2 \cdot 1}$

Factor $b$ out of $- 2 b - 1 \cdot 2 \cdot 1 b$ .

Factor $b$ out of $- 2 b$ .

$a = \frac{2 b \pm \sqrt{0 (b \cdot - 2 - 1 \cdot 2 \cdot (1 b))}}{2 \cdot 1}$

Factor $b$ out of $- 1 \cdot 2 \cdot 1 b$ .

$a = \frac{2 b \pm \sqrt{0 (b \cdot - 2 + b (- 1 \cdot 2 \cdot 1))}}{2 \cdot 1}$

Factor $b$ out of $b \cdot - 2 + b (- 1 \cdot 2 \cdot 1)$ .

$a = \frac{2 b \pm \sqrt{0 (b (- 2 - 1 \cdot 2 \cdot 1))}}{2 \cdot 1}$

Multiply $- 1$ by $2$ .

$a = \frac{2 b \pm \sqrt{0 (b (- 2 - 2 \cdot 1))}}{2 \cdot 1}$

Multiply $- 2$ by $1$ .

$a = \frac{2 b \pm \sqrt{0 (b (- 2 - 2))}}{2 \cdot 1}$

Subtract $2$ from $- 2$ .

$a = \frac{2 b \pm \sqrt{0 b \cdot - 4}}{2 \cdot 1}$

Combine exponents.

Multiply $0$ by $b$ .

$a = \frac{2 b \pm \sqrt{0 \cdot - 4}}{2 \cdot 1}$

Multiply $0$ by $- 4$ .

$a = \frac{2 b \pm \sqrt{0}}{2 \cdot 1}$

Rewrite $0$ as $0^{2}$ .

$a = \frac{2 b \pm \sqrt{0^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$a = \frac{2 b \pm 0}{2 \cdot 1}$

$2 b$ plus or minus $0$ is $2 b$ .

$a = \frac{2 b}{2 \cdot 1}$

Multiply $2$ by $1$ .

$a = \frac{2 b}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$a = \frac{2 b}{2}$

Divide $b$ by $1$ .

$a = b$

Solve Using the Quadratic Formula a^2-2ab+b^2

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