Basic Math Examples

$a (a + 1) (a + 2) (a + 3) + 1$

Step 1

Apply the distributive property.

$(a \cdot a + a \cdot 1) (a + 2) (a + 3) + 1$

Step 2

Multiply $a$ by $a$ .

$(a^{2} + a \cdot 1) (a + 2) (a + 3) + 1$

Step 3

Multiply $a$ by $1$ .

$(a^{2} + a) (a + 2) (a + 3) + 1$

Step 4

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

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Step 4.1

Apply the distributive property.

$(a^{2} (a + 2) + a (a + 2)) (a + 3) + 1$

Step 4.2

Apply the distributive property.

$(a^{2} a + a^{2} \cdot 2 + a (a + 2)) (a + 3) + 1$

Step 4.3

Apply the distributive property.

$(a^{2} a + a^{2} \cdot 2 + a \cdot a + a \cdot 2) (a + 3) + 1$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $a^{2}$ by $a$ by adding the exponents.

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Step 5.1.1.1

Multiply $a^{2}$ by $a$ .

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Step 5.1.1.1.1

Raise $a$ to the power of $1$ .

$(a^{2} a^{1} + a^{2} \cdot 2 + a \cdot a + a \cdot 2) (a + 3) + 1$

Step 5.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(a^{2 + 1} + a^{2} \cdot 2 + a \cdot a + a \cdot 2) (a + 3) + 1$

Step 5.1.1.2

Add $2$ and $1$ .

$(a^{3} + a^{2} \cdot 2 + a \cdot a + a \cdot 2) (a + 3) + 1$

Step 5.1.2

Move $2$ to the left of $a^{2}$ .

$(a^{3} + 2 \cdot a^{2} + a \cdot a + a \cdot 2) (a + 3) + 1$

Step 5.1.3

Multiply $a$ by $a$ .

$(a^{3} + 2 a^{2} + a^{2} + a \cdot 2) (a + 3) + 1$

Step 5.1.4

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

$(a^{3} + 2 a^{2} + a^{2} + 2 a) (a + 3) + 1$

Step 5.2

Add $2 a^{2}$ and $a^{2}$ .

$(a^{3} + 3 a^{2} + 2 a) (a + 3) + 1$

Step 6

Expand $(a^{3} + 3 a^{2} + 2 a) (a + 3)$ by multiplying each term in the first expression by each term in the second expression.

$a^{3} a + a^{3} \cdot 3 + 3 a^{2} a + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7

Simplify each term.

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Step 7.1

Multiply $a^{3}$ by $a$ by adding the exponents.

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Step 7.1.1

Multiply $a^{3}$ by $a$ .

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Step 7.1.1.1

Raise $a$ to the power of $1$ .

$a^{3} a^{1} + a^{3} \cdot 3 + 3 a^{2} a + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{3 + 1} + a^{3} \cdot 3 + 3 a^{2} a + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.1.2

Add $3$ and $1$ .

$a^{4} + a^{3} \cdot 3 + 3 a^{2} a + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.2

Move $3$ to the left of $a^{3}$ .

$a^{4} + 3 \cdot a^{3} + 3 a^{2} a + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.3

Multiply $a^{2}$ by $a$ by adding the exponents.

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Step 7.3.1

Move $a$ .

$a^{4} + 3 a^{3} + 3 (a \cdot a^{2}) + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.3.2

Multiply $a$ by $a^{2}$ .

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Step 7.3.2.1

Raise $a$ to the power of $1$ .

$a^{4} + 3 a^{3} + 3 (a^{1} a^{2}) + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{4} + 3 a^{3} + 3 a^{1 + 2} + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.3.3

Add $1$ and $2$ .

$a^{4} + 3 a^{3} + 3 a^{3} + 3 a^{2} \cdot 3 + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.4

Multiply $3$ by $3$ .

$a^{4} + 3 a^{3} + 3 a^{3} + 9 a^{2} + 2 a \cdot a + 2 a \cdot 3 + 1$

Step 7.5

Multiply $a$ by $a$ by adding the exponents.

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Step 7.5.1

Move $a$ .

$a^{4} + 3 a^{3} + 3 a^{3} + 9 a^{2} + 2 (a \cdot a) + 2 a \cdot 3 + 1$

Step 7.5.2

Multiply $a$ by $a$ .

$a^{4} + 3 a^{3} + 3 a^{3} + 9 a^{2} + 2 a^{2} + 2 a \cdot 3 + 1$

Step 7.6

Multiply $3$ by $2$ .

$a^{4} + 3 a^{3} + 3 a^{3} + 9 a^{2} + 2 a^{2} + 6 a + 1$

Step 8

Add $3 a^{3}$ and $3 a^{3}$ .

$a^{4} + 6 a^{3} + 9 a^{2} + 2 a^{2} + 6 a + 1$

Step 9

Add $9 a^{2}$ and $2 a^{2}$ .

$a^{4} + 6 a^{3} + 11 a^{2} + 6 a + 1$