Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

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

Step 2.1.2.2

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

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

Step 2.1.2.3

Add $2$ and $3$ .

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

Step 2.1.3

Move $- 1$ to the left of $x^{3}$ .

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

Step 2.1.4

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

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

Step 2.1.5

Rewrite using the commutative property of multiplication.

$3 x^{5} - x^{3} + 2 \cdot 3 x^{2} x^{2} + 2 x^{2} \cdot - 1$

Step 2.1.6

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

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Step 2.1.6.1

Move $x^{2}$ .

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

Step 2.1.6.2

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

$3 x^{5} - x^{3} + 2 \cdot 3 x^{2 + 2} + 2 x^{2} \cdot - 1$

Step 2.1.6.3

Add $2$ and $2$ .

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

Step 2.1.7

Multiply $2$ by $3$ .

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

Step 2.1.8

Multiply $- 1$ by $2$ .

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

Step 2.2

Move $- x^{3}$ .

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