Algebra Examples

{(a - b)}^{2}

${(a - b)}^{2}$

Step 1

Rewrite

{(a - b)}^{2}

${(a - b)}^{2}$ as

(a - b) (a - b)

$(a - b) (a - b)$ .

(a - b) (a - b)

$(a - b) (a - b)$

Step 2

Expand

(a - b) (a - b)

$(a - b) (a - b)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

a (a - b) - b (a - b)

$a (a - b) - b (a - b)$

Step 2.2

Apply the distributive property.

a \cdot a + a (- b) - b (a - b)

$a \cdot a + a (- b) - b (a - b)$

Step 2.3

Apply the distributive property.

a \cdot a + a (- b) - b a - b (- b)

$a \cdot a + a (- b) - b a - b (- b)$

a \cdot a + a (- b) - b a - b (- b)

$a \cdot a + a (- b) - b a - b (- b)$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply

a

$a$ by

a

$a$ .

a^{2} + a (- b) - b a - b (- b)

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

a^{2} - a b - b a - b (- b)

$a^{2} - a b - b a - b (- b)$

Step 3.1.3

Rewrite using the commutative property of multiplication.

a^{2} - a b - b a - 1 \cdot - 1 b \cdot b

$a^{2} - a b - b a - 1 \cdot - 1 b \cdot b$

Step 3.1.4

Multiply

b

$b$ by

b

$b$ by adding the exponents.

Tap for more steps...

Step 3.1.4.1

Move

b

$b$ .

a^{2} - a b - b a - 1 \cdot - 1 (b \cdot b)

$a^{2} - a b - b a - 1 \cdot - 1 (b \cdot b)$

Step 3.1.4.2

Multiply

b

$b$ by

b

$b$ .

a^{2} - a b - b a - 1 \cdot - 1 b^{2}

$a^{2} - a b - b a - 1 \cdot - 1 b^{2}$

a^{2} - a b - b a - 1 \cdot - 1 b^{2}

$a^{2} - a b - b a - 1 \cdot - 1 b^{2}$

Step 3.1.5

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

Step 3.1.6

Multiply

b^{2}

$b^{2}$ by

1

$1$ .

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

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

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

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

Step 3.2

Subtract

b a

$b a$ from

- a b

$- a b$ .

Tap for more steps...

Step 3.2.1

Move

b

$b$ .

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

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

Step 3.2.2

Subtract

a b

$a b$ from

- a b

$- a b$ .

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

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

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

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

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

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

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$