Basic Math Examples

$(7 r - 1) (r^{3} - r - 2)$

Step 1

Expand $(7 r - 1) (r^{3} - r - 2)$ by multiplying each term in the first expression by each term in the second expression.

$7 r \cdot r^{3} + 7 r (- r) + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $r^{3}$ .

$7 (r^{3} r) + 7 r (- r) + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

$7 (r^{3} r^{1}) + 7 r (- r) + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.1.2.2

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

$7 r^{3 + 1} + 7 r (- r) + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.1.3

Add $3$ and $1$ .

$7 r^{4} + 7 r (- r) + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$7 r^{4} + 7 \cdot - 1 r \cdot r + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.3

Multiply $r$ by $r$ by adding the exponents.

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Step 2.1.3.1

Move $r$ .

$7 r^{4} + 7 \cdot - 1 (r \cdot r) + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.3.2

Multiply $r$ by $r$ .

$7 r^{4} + 7 \cdot - 1 r^{2} + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.4

Multiply $7$ by $- 1$ .

$7 r^{4} - 7 r^{2} + 7 r \cdot - 2 - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.5

Multiply $- 2$ by $7$ .

$7 r^{4} - 7 r^{2} - 14 r - 1 r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.6

Rewrite $- 1 r^{3}$ as $- r^{3}$ .

$7 r^{4} - 7 r^{2} - 14 r - r^{3} - 1 (- r) - 1 \cdot - 2$

Step 2.1.7

Multiply $- 1 (- r)$ .

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Step 2.1.7.1

Multiply $- 1$ by $- 1$ .

$7 r^{4} - 7 r^{2} - 14 r - r^{3} + 1 r - 1 \cdot - 2$

Step 2.1.7.2

Multiply $r$ by $1$ .

$7 r^{4} - 7 r^{2} - 14 r - r^{3} + r - 1 \cdot - 2$

Step 2.1.8

Multiply $- 1$ by $- 2$ .

$7 r^{4} - 7 r^{2} - 14 r - r^{3} + r + 2$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 14 r$ and $r$ .

$7 r^{4} - 7 r^{2} - r^{3} - 13 r + 2$

Step 2.2.2

Move $- 7 r^{2}$ .

$7 r^{4} - r^{3} - 7 r^{2} - 13 r + 2$