Pre-Algebra Examples

$(x + 1) (2 x - 1) (x + 3)$

Step 1

Expand $(x + 1) (2 x - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(x (2 x - 1) + 1 (2 x - 1)) (x + 3)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

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

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

Step 2.1.4

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

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

Step 2.1.5

Multiply $2 x$ by $1$ .

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

Step 2.1.6

Multiply $- 1$ by $1$ .

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

Step 2.2

Add $- x$ and $2 x$ .

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

Step 3

Expand $(2 x^{2} + x - 1) (x + 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

Move $x$ .

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

Step 4.1.1.2

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

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Step 4.1.1.2.1

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

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

Step 4.1.1.2.2

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

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

Step 4.1.1.3

Add $1$ and $2$ .

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

Step 4.1.2

Multiply $3$ by $2$ .

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

Step 4.1.3

Multiply $x$ by $x$ .

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

Step 4.1.4

Move $3$ to the left of $x$ .

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

Step 4.1.5

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

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

Step 4.1.6

Multiply $- 1$ by $3$ .

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

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Add $6 x^{2}$ and $x^{2}$ .

$2 x^{3} + 7 x^{2} + 3 x - x - 3$

Step 4.2.2

Subtract $x$ from $3 x$ .

$2 x^{3} + 7 x^{2} + 2 x - 3$