Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Expand $(a + 2) (a + 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

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 $a$ .

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

Step 1.3.1.2

Move $2$ to the left of $a$ .

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

Step 1.3.1.3

Multiply $2$ by $2$ .

$a^{2} + 2 a + 2 a + 4 - {(b + 1)}^{2}$

Step 1.3.2

Add $2 a$ and $2 a$ .

$a^{2} + 4 a + 4 - {(b + 1)}^{2}$

Step 1.4

Rewrite ${(b + 1)}^{2}$ as $(b + 1) (b + 1)$ .

$a^{2} + 4 a + 4 - ((b + 1) (b + 1))$

Step 1.5

Expand $(b + 1) (b + 1)$ using the FOIL Method.

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Step 1.5.1

Apply the distributive property.

$a^{2} + 4 a + 4 - (b (b + 1) + 1 (b + 1))$

Step 1.5.2

Apply the distributive property.

$a^{2} + 4 a + 4 - (b \cdot b + b \cdot 1 + 1 (b + 1))$

Step 1.5.3

Apply the distributive property.

$a^{2} + 4 a + 4 - (b \cdot b + b \cdot 1 + 1 b + 1 \cdot 1)$

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 $b$ by $b$ .

$a^{2} + 4 a + 4 - (b^{2} + b \cdot 1 + 1 b + 1 \cdot 1)$

Step 1.6.1.2

Multiply $b$ by $1$ .

$a^{2} + 4 a + 4 - (b^{2} + b + 1 b + 1 \cdot 1)$

Step 1.6.1.3

Multiply $b$ by $1$ .

$a^{2} + 4 a + 4 - (b^{2} + b + b + 1 \cdot 1)$

Step 1.6.1.4

Multiply $1$ by $1$ .

$a^{2} + 4 a + 4 - (b^{2} + b + b + 1)$

Step 1.6.2

Add $b$ and $b$ .

$a^{2} + 4 a + 4 - (b^{2} + 2 b + 1)$

Step 1.7

Apply the distributive property.

$a^{2} + 4 a + 4 - b^{2} - (2 b) - 1 \cdot 1$

Step 1.8

Simplify.

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Step 1.8.1

Multiply $2$ by $- 1$ .

$a^{2} + 4 a + 4 - b^{2} - 2 b - 1 \cdot 1$

Step 1.8.2

Multiply $- 1$ by $1$ .

$a^{2} + 4 a + 4 - b^{2} - 2 b - 1$

Step 2

Simplify the expression.

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Step 2.1

Subtract $1$ from $4$ .

$a^{2} + 4 a - b^{2} - 2 b + 3$

Step 2.2

Move $4 a$ .

$a^{2} - b^{2} + 4 a - 2 b + 3$