Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $a$ by $a$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

Rewrite using the commutative property of multiplication.

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

Step 2.1.4

Multiply $b$ by $b$ by adding the exponents.

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Step 2.1.4.1

Move $b$ .

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

Step 2.1.4.2

Multiply $b$ by $b$ .

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

Step 2.1.5

Multiply $- 1$ by $- 1$ .

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

Step 2.1.6

Multiply $b^{2}$ by $1$ .

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

Step 2.2

Subtract $b a$ from $- a b$ .

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Step 2.2.1

Move $b$ .

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

Step 2.2.2

Subtract $a b$ from $- a b$ .

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