Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$2 x^{2} x + 2 x^{2} \cdot 4 + 3 x + 3 \cdot 4$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

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

Step 2.1.2

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

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Step 2.1.2.1

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

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

Step 2.1.2.2

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

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

Step 2.1.3

Add $1$ and $2$ .

$2 x^{3} + 2 x^{2} \cdot 4 + 3 x + 3 \cdot 4$

Step 2.2

Multiply $4$ by $2$ .

$2 x^{3} + 8 x^{2} + 3 x + 3 \cdot 4$

Step 2.3

Multiply $3$ by $4$ .

$2 x^{3} + 8 x^{2} + 3 x + 12$