Precalculus Examples

$(x + 7) (x^{2} + 5 x + 9)$

Step 1

Expand $(x + 7) (x^{2} + 5 x + 9)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (5 x) + x \cdot 9 + 7 x^{2} + 7 (5 x) + 7 \cdot 9$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

$x^{1} x^{2} + x (5 x) + x \cdot 9 + 7 x^{2} + 7 (5 x) + 7 \cdot 9$

Step 2.1.1.1.2

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

$x^{1 + 2} + x (5 x) + x \cdot 9 + 7 x^{2} + 7 (5 x) + 7 \cdot 9$

Step 2.1.1.2

Add $1$ and $2$ .

$x^{3} + x (5 x) + x \cdot 9 + 7 x^{2} + 7 (5 x) + 7 \cdot 9$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$x^{3} + 5 x \cdot x + x \cdot 9 + 7 x^{2} + 7 (5 x) + 7 \cdot 9$

Step 2.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.3.1

Move $x$ .

$x^{3} + 5 (x \cdot x) + x \cdot 9 + 7 x^{2} + 7 (5 x) + 7 \cdot 9$

Step 2.1.3.2

Multiply $x$ by $x$ .

$x^{3} + 5 x^{2} + x \cdot 9 + 7 x^{2} + 7 (5 x) + 7 \cdot 9$

Step 2.1.4

Move $9$ to the left of $x$ .

$x^{3} + 5 x^{2} + 9 \cdot x + 7 x^{2} + 7 (5 x) + 7 \cdot 9$

Step 2.1.5

Multiply $5$ by $7$ .

$x^{3} + 5 x^{2} + 9 x + 7 x^{2} + 35 x + 7 \cdot 9$

Step 2.1.6

Multiply $7$ by $9$ .

$x^{3} + 5 x^{2} + 9 x + 7 x^{2} + 35 x + 63$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $5 x^{2}$ and $7 x^{2}$ .

$x^{3} + 12 x^{2} + 9 x + 35 x + 63$

Step 2.2.2

Add $9 x$ and $35 x$ .

$x^{3} + 12 x^{2} + 44 x + 63$