Precalculus Examples

$(1 + 8 x) (x^{2} - 9 x + 1)$

Step 1

Expand $(1 + 8 x) (x^{2} - 9 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$1 x^{2} + 1 (- 9 x) + 1 \cdot 1 + 8 x \cdot x^{2} + 8 x (- 9 x) + 8 x \cdot 1$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$x^{2} + 1 (- 9 x) + 1 \cdot 1 + 8 x \cdot x^{2} + 8 x (- 9 x) + 8 x \cdot 1$

Step 2.1.2

Multiply $- 9 x$ by $1$ .

$x^{2} - 9 x + 1 \cdot 1 + 8 x \cdot x^{2} + 8 x (- 9 x) + 8 x \cdot 1$

Step 2.1.3

Multiply $1$ by $1$ .

$x^{2} - 9 x + 1 + 8 x \cdot x^{2} + 8 x (- 9 x) + 8 x \cdot 1$

Step 2.1.4

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

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Step 2.1.4.1

Move $x^{2}$ .

$x^{2} - 9 x + 1 + 8 (x^{2} x) + 8 x (- 9 x) + 8 x \cdot 1$

Step 2.1.4.2

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

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Step 2.1.4.2.1

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

$x^{2} - 9 x + 1 + 8 (x^{2} x^{1}) + 8 x (- 9 x) + 8 x \cdot 1$

Step 2.1.4.2.2

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

$x^{2} - 9 x + 1 + 8 x^{2 + 1} + 8 x (- 9 x) + 8 x \cdot 1$

Step 2.1.4.3

Add $2$ and $1$ .

$x^{2} - 9 x + 1 + 8 x^{3} + 8 x (- 9 x) + 8 x \cdot 1$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$x^{2} - 9 x + 1 + 8 x^{3} + 8 \cdot - 9 x \cdot x + 8 x \cdot 1$

Step 2.1.6

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

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Step 2.1.6.1

Move $x$ .

$x^{2} - 9 x + 1 + 8 x^{3} + 8 \cdot - 9 (x \cdot x) + 8 x \cdot 1$

Step 2.1.6.2

Multiply $x$ by $x$ .

$x^{2} - 9 x + 1 + 8 x^{3} + 8 \cdot - 9 x^{2} + 8 x \cdot 1$

Step 2.1.7

Multiply $8$ by $- 9$ .

$x^{2} - 9 x + 1 + 8 x^{3} - 72 x^{2} + 8 x \cdot 1$

Step 2.1.8

Multiply $8$ by $1$ .

$x^{2} - 9 x + 1 + 8 x^{3} - 72 x^{2} + 8 x$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $72 x^{2}$ from $x^{2}$ .

$- 71 x^{2} - 9 x + 1 + 8 x^{3} + 8 x$

Step 2.2.2

Add $- 9 x$ and $8 x$ .

$- 71 x^{2} - x + 1 + 8 x^{3}$

Step 2.2.3

Simplify the expression.

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Step 2.2.3.1

Move $1$ .

$- 71 x^{2} - x + 8 x^{3} + 1$

Step 2.2.3.2

Move $- x$ .

$- 71 x^{2} + 8 x^{3} - x + 1$

Step 2.2.3.3

Reorder $- 71 x^{2}$ and $8 x^{3}$ .

$8 x^{3} - 71 x^{2} - x + 1$