Basic Math Examples

${(a + 1)}^{2} + 2 (a + 1) - 5$

Step 1

Simplify each term.

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Step 1.1

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

$(a + 1) (a + 1) + 2 (a + 1) - 5$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$a (a + 1) + 1 (a + 1) + 2 (a + 1) - 5$

Step 1.2.2

Apply the distributive property.

$a \cdot a + a \cdot 1 + 1 (a + 1) + 2 (a + 1) - 5$

Step 1.2.3

Apply the distributive property.

$a \cdot a + a \cdot 1 + 1 a + 1 \cdot 1 + 2 (a + 1) - 5$

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 $a$ .

$a^{2} + a \cdot 1 + 1 a + 1 \cdot 1 + 2 (a + 1) - 5$

Step 1.3.1.2

Multiply $a$ by $1$ .

$a^{2} + a + 1 a + 1 \cdot 1 + 2 (a + 1) - 5$

Step 1.3.1.3

Multiply $a$ by $1$ .

$a^{2} + a + a + 1 \cdot 1 + 2 (a + 1) - 5$

Step 1.3.1.4

Multiply $1$ by $1$ .

$a^{2} + a + a + 1 + 2 (a + 1) - 5$

Step 1.3.2

Add $a$ and $a$ .

$a^{2} + 2 a + 1 + 2 (a + 1) - 5$

Step 1.4

Apply the distributive property.

$a^{2} + 2 a + 1 + 2 a + 2 \cdot 1 - 5$

Step 1.5

Multiply $2$ by $1$ .

$a^{2} + 2 a + 1 + 2 a + 2 - 5$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2 a$ and $2 a$ .

$a^{2} + 4 a + 1 + 2 - 5$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Add $1$ and $2$ .

$a^{2} + 4 a + 3 - 5$

Step 2.2.2

Subtract $5$ from $3$ .

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