Algebra Examples

$(2 x + 3) \cdot x \cdot (4 x + 1)$

Step 1

Apply the distributive property.

$(2 x \cdot x + 3 x) \cdot (4 x + 1)$

Step 2

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

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Step 2.1

Move $x$ .

$(2 (x \cdot x) + 3 x) \cdot (4 x + 1)$

Step 2.2

Multiply $x$ by $x$ .

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

Step 3

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

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Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Rewrite using the commutative property of multiplication.

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

Step 4.1.2

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

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Step 4.1.2.1

Move $x$ .

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

Step 4.1.2.2

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

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Step 4.1.2.2.1

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

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

Step 4.1.2.2.2

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

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

Step 4.1.2.3

Add $1$ and $2$ .

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

Step 4.1.3

Multiply $2$ by $4$ .

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

Step 4.1.4

Multiply $2$ by $1$ .

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

Step 4.1.5

Rewrite using the commutative property of multiplication.

$8 x^{3} + 2 x^{2} + 3 \cdot 4 x \cdot x + 3 x \cdot 1$

Step 4.1.6

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

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Step 4.1.6.1

Move $x$ .

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

Step 4.1.6.2

Multiply $x$ by $x$ .

$8 x^{3} + 2 x^{2} + 3 \cdot 4 x^{2} + 3 x \cdot 1$

Step 4.1.7

Multiply $3$ by $4$ .

$8 x^{3} + 2 x^{2} + 12 x^{2} + 3 x \cdot 1$

Step 4.1.8

Multiply $3$ by $1$ .

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

Step 4.2

Add $2 x^{2}$ and $12 x^{2}$ .

$8 x^{3} + 14 x^{2} + 3 x$