Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

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

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Step 2.2.1

Move $x^{2}$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $2$ and $1$ .

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

Step 2.3

Multiply $3$ by $2$ .

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

Step 2.4

Multiply $5$ by $3$ .

$6 x^{3} + 15 x - 2 (2 x^{2}) - 2 \cdot 5$

Step 2.5

Multiply $2$ by $- 2$ .

$6 x^{3} + 15 x - 4 x^{2} - 2 \cdot 5$

Step 2.6

Multiply $- 2$ by $5$ .

$6 x^{3} + 15 x - 4 x^{2} - 10$