Algebra Examples

$(x^{4}) (3 x^{3} - 2) (4 x^{2} + 5 x)$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$(x^{4} (3 x^{3}) + x^{4} \cdot - 2) (4 x^{2} + 5 x)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$(3 x^{4} x^{3} + x^{4} \cdot - 2) (4 x^{2} + 5 x)$

Step 1.2.2

Move $- 2$ to the left of $x^{4}$ .

$(3 x^{4} x^{3} - 2 \cdot x^{4}) (4 x^{2} + 5 x)$

Step 1.3

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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Step 1.3.1

Move $x^{3}$ .

$(3 (x^{3} x^{4}) - 2 \cdot x^{4}) (4 x^{2} + 5 x)$

Step 1.3.2

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

$(3 x^{3 + 4} - 2 \cdot x^{4}) (4 x^{2} + 5 x)$

Step 1.3.3

Add $3$ and $4$ .

$(3 x^{7} - 2 \cdot x^{4}) (4 x^{2} + 5 x)$

$(3 x^{7} - 2 x^{4}) (4 x^{2} + 5 x)$

Step 2

Expand $(3 x^{7} - 2 x^{4}) (4 x^{2} + 5 x)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$3 x^{7} (4 x^{2} + 5 x) - 2 x^{4} (4 x^{2} + 5 x)$

Step 2.2

Apply the distributive property.

$3 x^{7} (4 x^{2}) + 3 x^{7} (5 x) - 2 x^{4} (4 x^{2} + 5 x)$

Step 2.3

Apply the distributive property.

$3 x^{7} (4 x^{2}) + 3 x^{7} (5 x) - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3

Simplify each term.

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Step 3.1

Rewrite using the commutative property of multiplication.

$3 \cdot 4 x^{7} x^{2} + 3 x^{7} (5 x) - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.2

Multiply $x^{7}$ by $x^{2}$ by adding the exponents.

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Step 3.2.1

Move $x^{2}$ .

$3 \cdot 4 (x^{2} x^{7}) + 3 x^{7} (5 x) - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.2.2

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

$3 \cdot 4 x^{2 + 7} + 3 x^{7} (5 x) - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.2.3

Add $2$ and $7$ .

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

Step 3.3

Multiply $3$ by $4$ .

$12 x^{9} + 3 x^{7} (5 x) - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.4

Rewrite using the commutative property of multiplication.

$12 x^{9} + 3 \cdot 5 x^{7} x - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.5

Multiply $x^{7}$ by $x$ by adding the exponents.

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Step 3.5.1

Move $x$ .

$12 x^{9} + 3 \cdot 5 (x \cdot x^{7}) - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.5.2

Multiply $x$ by $x^{7}$ .

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Step 3.5.2.1

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

$12 x^{9} + 3 \cdot 5 (x^{1} x^{7}) - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.5.2.2

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

$12 x^{9} + 3 \cdot 5 x^{1 + 7} - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.5.3

Add $1$ and $7$ .

$12 x^{9} + 3 \cdot 5 x^{8} - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.6

Multiply $3$ by $5$ .

$12 x^{9} + 15 x^{8} - 2 x^{4} (4 x^{2}) - 2 x^{4} (5 x)$

Step 3.7

Rewrite using the commutative property of multiplication.

$12 x^{9} + 15 x^{8} - 2 \cdot 4 x^{4} x^{2} - 2 x^{4} (5 x)$

Step 3.8

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Step 3.8.1

Move $x^{2}$ .

$12 x^{9} + 15 x^{8} - 2 \cdot 4 (x^{2} x^{4}) - 2 x^{4} (5 x)$

Step 3.8.2

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

$12 x^{9} + 15 x^{8} - 2 \cdot 4 x^{2 + 4} - 2 x^{4} (5 x)$

Step 3.8.3

Add $2$ and $4$ .

$12 x^{9} + 15 x^{8} - 2 \cdot 4 x^{6} - 2 x^{4} (5 x)$

Step 3.9

Multiply $- 2$ by $4$ .

$12 x^{9} + 15 x^{8} - 8 x^{6} - 2 x^{4} (5 x)$

Step 3.10

Rewrite using the commutative property of multiplication.

$12 x^{9} + 15 x^{8} - 8 x^{6} - 2 \cdot 5 x^{4} x$

Step 3.11

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 3.11.1

Move $x$ .

$12 x^{9} + 15 x^{8} - 8 x^{6} - 2 \cdot 5 (x \cdot x^{4})$

Step 3.11.2

Multiply $x$ by $x^{4}$ .

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Step 3.11.2.1

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

$12 x^{9} + 15 x^{8} - 8 x^{6} - 2 \cdot 5 (x^{1} x^{4})$

Step 3.11.2.2

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

$12 x^{9} + 15 x^{8} - 8 x^{6} - 2 \cdot 5 x^{1 + 4}$

Step 3.11.3

Add $1$ and $4$ .

$12 x^{9} + 15 x^{8} - 8 x^{6} - 2 \cdot 5 x^{5}$

Step 3.12

Multiply $- 2$ by $5$ .

$12 x^{9} + 15 x^{8} - 8 x^{6} - 10 x^{5}$