Algebra Examples

$(4 x^{3} + x) (2 x^{2} - 1) (6 x - 3)$

Step 1

Expand $(4 x^{3} + x) (2 x^{2} - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(4 x^{3} (2 x^{2} - 1) + x (2 x^{2} - 1)) (6 x - 3)$

Step 1.2

Apply the distributive property.

$(4 x^{3} (2 x^{2}) + 4 x^{3} \cdot - 1 + x (2 x^{2} - 1)) (6 x - 3)$

Step 1.3

Apply the distributive property.

$(4 x^{3} (2 x^{2}) + 4 x^{3} \cdot - 1 + x (2 x^{2}) + x \cdot - 1) (6 x - 3)$

Step 2

Simplify and combine like 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.

$(4 \cdot 2 x^{3} x^{2} + 4 x^{3} \cdot - 1 + x (2 x^{2}) + x \cdot - 1) (6 x - 3)$

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

$(4 \cdot 2 (x^{2} x^{3}) + 4 x^{3} \cdot - 1 + x (2 x^{2}) + x \cdot - 1) (6 x - 3)$

Step 2.1.2.2

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

$(4 \cdot 2 x^{2 + 3} + 4 x^{3} \cdot - 1 + x (2 x^{2}) + x \cdot - 1) (6 x - 3)$

Step 2.1.2.3

Add $2$ and $3$ .

$(4 \cdot 2 x^{5} + 4 x^{3} \cdot - 1 + x (2 x^{2}) + x \cdot - 1) (6 x - 3)$

Step 2.1.3

Multiply $4$ by $2$ .

$(8 x^{5} + 4 x^{3} \cdot - 1 + x (2 x^{2}) + x \cdot - 1) (6 x - 3)$

Step 2.1.4

Multiply $- 1$ by $4$ .

$(8 x^{5} - 4 x^{3} + x (2 x^{2}) + x \cdot - 1) (6 x - 3)$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$(8 x^{5} - 4 x^{3} + 2 x \cdot x^{2} + x \cdot - 1) (6 x - 3)$

Step 2.1.6

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

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Step 2.1.6.1

Move $x^{2}$ .

$(8 x^{5} - 4 x^{3} + 2 (x^{2} x) + x \cdot - 1) (6 x - 3)$

Step 2.1.6.2

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

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Step 2.1.6.2.1

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

$(8 x^{5} - 4 x^{3} + 2 (x^{2} x^{1}) + x \cdot - 1) (6 x - 3)$

Step 2.1.6.2.2

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

$(8 x^{5} - 4 x^{3} + 2 x^{2 + 1} + x \cdot - 1) (6 x - 3)$

Step 2.1.6.3

Add $2$ and $1$ .

$(8 x^{5} - 4 x^{3} + 2 x^{3} + x \cdot - 1) (6 x - 3)$

Step 2.1.7

Move $- 1$ to the left of $x$ .

$(8 x^{5} - 4 x^{3} + 2 x^{3} - 1 \cdot x) (6 x - 3)$

Step 2.1.8

Rewrite $- 1 x$ as $- x$ .

$(8 x^{5} - 4 x^{3} + 2 x^{3} - x) (6 x - 3)$

Step 2.2

Add $- 4 x^{3}$ and $2 x^{3}$ .

$(8 x^{5} - 2 x^{3} - x) (6 x - 3)$

Step 3

Expand $(8 x^{5} - 2 x^{3} - x) (6 x - 3)$ by multiplying each term in the first expression by each term in the second expression.

$8 x^{5} (6 x) + 8 x^{5} \cdot - 3 - 2 x^{3} (6 x) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4

Simplify each term.

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Step 4.1

Rewrite using the commutative property of multiplication.

$8 \cdot 6 x^{5} x + 8 x^{5} \cdot - 3 - 2 x^{3} (6 x) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.2

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

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Step 4.2.1

Move $x$ .

$8 \cdot 6 (x \cdot x^{5}) + 8 x^{5} \cdot - 3 - 2 x^{3} (6 x) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.2.2

Multiply $x$ by $x^{5}$ .

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Step 4.2.2.1

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

$8 \cdot 6 (x^{1} x^{5}) + 8 x^{5} \cdot - 3 - 2 x^{3} (6 x) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.2.2.2

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

$8 \cdot 6 x^{1 + 5} + 8 x^{5} \cdot - 3 - 2 x^{3} (6 x) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.2.3

Add $1$ and $5$ .

$8 \cdot 6 x^{6} + 8 x^{5} \cdot - 3 - 2 x^{3} (6 x) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.3

Multiply $8$ by $6$ .

$48 x^{6} + 8 x^{5} \cdot - 3 - 2 x^{3} (6 x) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.4

Multiply $- 3$ by $8$ .

$48 x^{6} - 24 x^{5} - 2 x^{3} (6 x) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.5

Rewrite using the commutative property of multiplication.

$48 x^{6} - 24 x^{5} - 2 \cdot 6 x^{3} x - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.6

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

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Step 4.6.1

Move $x$ .

$48 x^{6} - 24 x^{5} - 2 \cdot 6 (x \cdot x^{3}) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.6.2

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

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Step 4.6.2.1

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

$48 x^{6} - 24 x^{5} - 2 \cdot 6 (x^{1} x^{3}) - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.6.2.2

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

$48 x^{6} - 24 x^{5} - 2 \cdot 6 x^{1 + 3} - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.6.3

Add $1$ and $3$ .

$48 x^{6} - 24 x^{5} - 2 \cdot 6 x^{4} - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.7

Multiply $- 2$ by $6$ .

$48 x^{6} - 24 x^{5} - 12 x^{4} - 2 x^{3} \cdot - 3 - x (6 x) - x \cdot - 3$

Step 4.8

Multiply $- 3$ by $- 2$ .

$48 x^{6} - 24 x^{5} - 12 x^{4} + 6 x^{3} - x (6 x) - x \cdot - 3$

Step 4.9

Rewrite using the commutative property of multiplication.

$48 x^{6} - 24 x^{5} - 12 x^{4} + 6 x^{3} - 1 \cdot 6 x \cdot x - x \cdot - 3$

Step 4.10

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

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Step 4.10.1

Move $x$ .

$48 x^{6} - 24 x^{5} - 12 x^{4} + 6 x^{3} - 1 \cdot 6 (x \cdot x) - x \cdot - 3$

Step 4.10.2

Multiply $x$ by $x$ .

$48 x^{6} - 24 x^{5} - 12 x^{4} + 6 x^{3} - 1 \cdot 6 x^{2} - x \cdot - 3$

Step 4.11

Multiply $- 1$ by $6$ .

$48 x^{6} - 24 x^{5} - 12 x^{4} + 6 x^{3} - 6 x^{2} - x \cdot - 3$

Step 4.12

Multiply $- 3$ by $- 1$ .

$48 x^{6} - 24 x^{5} - 12 x^{4} + 6 x^{3} - 6 x^{2} + 3 x$