Algebra Examples

$(7 r^{2} - 6 r - 6) (2 r - 4)$

Step 1

Expand $(7 r^{2} - 6 r - 6) (2 r - 4)$ by multiplying each term in the first expression by each term in the second expression.

$7 r^{2} (2 r) + 7 r^{2} \cdot - 4 - 6 r (2 r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$7 \cdot 2 r^{2} r + 7 r^{2} \cdot - 4 - 6 r (2 r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.2

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

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Step 2.1.2.1

Move $r$ .

$7 \cdot 2 (r \cdot r^{2}) + 7 r^{2} \cdot - 4 - 6 r (2 r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$7 \cdot 2 (r^{1} r^{2}) + 7 r^{2} \cdot - 4 - 6 r (2 r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.2.2.2

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

$7 \cdot 2 r^{1 + 2} + 7 r^{2} \cdot - 4 - 6 r (2 r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.2.3

Add $1$ and $2$ .

$7 \cdot 2 r^{3} + 7 r^{2} \cdot - 4 - 6 r (2 r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.3

Multiply $7$ by $2$ .

$14 r^{3} + 7 r^{2} \cdot - 4 - 6 r (2 r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.4

Multiply $- 4$ by $7$ .

$14 r^{3} - 28 r^{2} - 6 r (2 r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$14 r^{3} - 28 r^{2} - 6 \cdot 2 r \cdot r - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.6

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

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Step 2.1.6.1

Move $r$ .

$14 r^{3} - 28 r^{2} - 6 \cdot 2 (r \cdot r) - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.6.2

Multiply $r$ by $r$ .

$14 r^{3} - 28 r^{2} - 6 \cdot 2 r^{2} - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.7

Multiply $- 6$ by $2$ .

$14 r^{3} - 28 r^{2} - 12 r^{2} - 6 r \cdot - 4 - 6 (2 r) - 6 \cdot - 4$

Step 2.1.8

Multiply $- 4$ by $- 6$ .

$14 r^{3} - 28 r^{2} - 12 r^{2} + 24 r - 6 (2 r) - 6 \cdot - 4$

Step 2.1.9

Multiply $2$ by $- 6$ .

$14 r^{3} - 28 r^{2} - 12 r^{2} + 24 r - 12 r - 6 \cdot - 4$

Step 2.1.10

Multiply $- 6$ by $- 4$ .

$14 r^{3} - 28 r^{2} - 12 r^{2} + 24 r - 12 r + 24$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $12 r^{2}$ from $- 28 r^{2}$ .

$14 r^{3} - 40 r^{2} + 24 r - 12 r + 24$

Step 2.2.2

Subtract $12 r$ from $24 r$ .

$14 r^{3} - 40 r^{2} + 12 r + 24$