Algebra Examples

$(- 2 x^{a - 2}) (7 x^{5} - 8 x^{2} + 6 x^{3} - 9 x + 2)$

Step 1

Apply the distributive property.

$- 2 x^{a - 2} (7 x^{5}) - 2 x^{a - 2} (- 8 x^{2}) - 2 x^{a - 2} (6 x^{3}) - 2 x^{a - 2} (- 9 x) - 2 x^{a - 2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 2 \cdot 7 x^{a - 2} x^{5} - 2 x^{a - 2} (- 8 x^{2}) - 2 x^{a - 2} (6 x^{3}) - 2 x^{a - 2} (- 9 x) - 2 x^{a - 2} \cdot 2$

Step 2.2

Rewrite using the commutative property of multiplication.

$- 2 \cdot 7 x^{a - 2} x^{5} - 2 \cdot - 8 x^{a - 2} x^{2} - 2 x^{a - 2} (6 x^{3}) - 2 x^{a - 2} (- 9 x) - 2 x^{a - 2} \cdot 2$

Step 2.3

Rewrite using the commutative property of multiplication.

$- 2 \cdot 7 x^{a - 2} x^{5} - 2 \cdot - 8 x^{a - 2} x^{2} - 2 \cdot 6 x^{a - 2} x^{3} - 2 x^{a - 2} (- 9 x) - 2 x^{a - 2} \cdot 2$

Step 2.4

Rewrite using the commutative property of multiplication.

$- 2 \cdot 7 x^{a - 2} x^{5} - 2 \cdot - 8 x^{a - 2} x^{2} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 2 x^{a - 2} \cdot 2$

Step 2.5

Multiply $2$ by $- 2$ .

$- 2 \cdot 7 x^{a - 2} x^{5} - 2 \cdot - 8 x^{a - 2} x^{2} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $x^{a - 2}$ by $x^{5}$ by adding the exponents.

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Step 3.1.1

Move $x^{5}$ .

$- 2 \cdot 7 (x^{5} x^{a - 2}) - 2 \cdot - 8 x^{a - 2} x^{2} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.1.2

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

$- 2 \cdot 7 x^{5 + a - 2} - 2 \cdot - 8 x^{a - 2} x^{2} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.1.3

Subtract $2$ from $5$ .

$- 2 \cdot 7 x^{a + 3} - 2 \cdot - 8 x^{a - 2} x^{2} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.2

Multiply $- 2$ by $7$ .

$- 14 x^{a + 3} - 2 \cdot - 8 x^{a - 2} x^{2} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.3

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

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Step 3.3.1

Move $x^{2}$ .

$- 14 x^{a + 3} - 2 \cdot - 8 (x^{2} x^{a - 2}) - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.3.2

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

$- 14 x^{a + 3} - 2 \cdot - 8 x^{2 + a - 2} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.3.3

Combine the opposite terms in $2 + a - 2$ .

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Step 3.3.3.1

Subtract $2$ from $2$ .

$- 14 x^{a + 3} - 2 \cdot - 8 x^{a + 0} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.3.3.2

Add $a$ and $0$ .

$- 14 x^{a + 3} - 2 \cdot - 8 x^{a} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.4

Multiply $- 2$ by $- 8$ .

$- 14 x^{a + 3} + 16 x^{a} - 2 \cdot 6 x^{a - 2} x^{3} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.5

Multiply $x^{a - 2}$ by $x^{3}$ by adding the exponents.

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Step 3.5.1

Move $x^{3}$ .

$- 14 x^{a + 3} + 16 x^{a} - 2 \cdot 6 (x^{3} x^{a - 2}) - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.5.2

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

$- 14 x^{a + 3} + 16 x^{a} - 2 \cdot 6 x^{3 + a - 2} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.5.3

Subtract $2$ from $3$ .

$- 14 x^{a + 3} + 16 x^{a} - 2 \cdot 6 x^{a + 1} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.6

Multiply $- 2$ by $6$ .

$- 14 x^{a + 3} + 16 x^{a} - 12 x^{a + 1} - 2 \cdot - 9 x^{a - 2} x - 4 x^{a - 2}$

Step 3.7

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

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Step 3.7.1

Move $x$ .

$- 14 x^{a + 3} + 16 x^{a} - 12 x^{a + 1} - 2 \cdot - 9 (x \cdot x^{a - 2}) - 4 x^{a - 2}$

Step 3.7.2

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

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Step 3.7.2.1

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

$- 14 x^{a + 3} + 16 x^{a} - 12 x^{a + 1} - 2 \cdot - 9 (x^{1} x^{a - 2}) - 4 x^{a - 2}$

Step 3.7.2.2

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

$- 14 x^{a + 3} + 16 x^{a} - 12 x^{a + 1} - 2 \cdot - 9 x^{1 + a - 2} - 4 x^{a - 2}$

Step 3.7.3

Subtract $2$ from $1$ .

$- 14 x^{a + 3} + 16 x^{a} - 12 x^{a + 1} - 2 \cdot - 9 x^{a - 1} - 4 x^{a - 2}$

Step 3.8

Multiply $- 2$ by $- 9$ .

$- 14 x^{a + 3} + 16 x^{a} - 12 x^{a + 1} + 18 x^{a - 1} - 4 x^{a - 2}$