Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(a + b)}^{2}$ as $(a + b) (a + b)$ .

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $a$ by $a$ .

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

Step 1.3.1.2

Multiply $b$ by $b$ .

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

Step 1.3.2

Add $a b$ and $b a$ .

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Step 1.3.2.1

Reorder $b$ and $a$ .

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

Step 1.3.2.2

Add $a b$ and $a b$ .

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

Step 1.4

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

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

Step 1.5

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

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Step 1.5.1

Apply the distributive property.

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

Step 1.5.2

Apply the distributive property.

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

Step 1.5.3

Apply the distributive property.

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

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Multiply $a$ by $a$ .

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

Step 1.6.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.6.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.6.1.4

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

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Step 1.6.1.4.1

Move $b$ .

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

Step 1.6.1.4.2

Multiply $b$ by $b$ .

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

Step 1.6.1.5

Multiply $- 1$ by $- 1$ .

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

Step 1.6.1.6

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

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

Step 1.6.2

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

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Step 1.6.2.1

Move $b$ .

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

Step 1.6.2.2

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

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

Step 1.7

Apply the distributive property.

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

Step 1.8

Multiply $- 2$ by $- 1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $a^{2} + 2 a b + b^{2} - a^{2} + 2 a b - b^{2}$ .

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Step 2.1.1

Subtract $a^{2}$ from $a^{2}$ .

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

Step 2.1.2

Add $2 a b + b^{2}$ and $0$ .

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

Step 2.1.3

Subtract $b^{2}$ from $b^{2}$ .

$2 a b + 2 a b + 0$

Step 2.1.4

Add $2 a b + 2 a b$ and $0$ .

$2 a b + 2 a b$

Step 2.2

Add $2 a b$ and $2 a b$ .

$4 a b$