Pre-Algebra Examples

$(x + 3) (x - 4) (6 x - 5)$

Step 1

Expand $(x + 3) (x - 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(x (x - 4) + 3 (x - 4)) (6 x - 5)$

Step 1.2

Apply the distributive property.

$(x \cdot x + x \cdot - 4 + 3 (x - 4)) (6 x - 5)$

Step 1.3

Apply the distributive property.

$(x \cdot x + x \cdot - 4 + 3 x + 3 \cdot - 4) (6 x - 5)$

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

Multiply $x$ by $x$ .

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

Step 2.1.2

Move $- 4$ to the left of $x$ .

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

Step 2.1.3

Multiply $3$ by $- 4$ .

$(x^{2} - 4 x + 3 x - 12) (6 x - 5)$

Step 2.2

Add $- 4 x$ and $3 x$ .

$(x^{2} - x - 12) (6 x - 5)$

Step 3

Expand $(x^{2} - x - 12) (6 x - 5)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} (6 x) + x^{2} \cdot - 5 - x (6 x) - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4

Simplify 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.

$6 x^{2} x + x^{2} \cdot - 5 - x (6 x) - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.2

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

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Step 4.1.2.1

Move $x$ .

$6 (x \cdot x^{2}) + x^{2} \cdot - 5 - x (6 x) - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

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 $1$ .

$6 (x^{1} x^{2}) + x^{2} \cdot - 5 - x (6 x) - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.2.2.2

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

$6 x^{1 + 2} + x^{2} \cdot - 5 - x (6 x) - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.2.3

Add $1$ and $2$ .

$6 x^{3} + x^{2} \cdot - 5 - x (6 x) - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.3

Move $- 5$ to the left of $x^{2}$ .

$6 x^{3} - 5 \cdot x^{2} - x (6 x) - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.4

Rewrite using the commutative property of multiplication.

$6 x^{3} - 5 x^{2} - 1 \cdot 6 x \cdot x - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.5

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

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Step 4.1.5.1

Move $x$ .

$6 x^{3} - 5 x^{2} - 1 \cdot 6 (x \cdot x) - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.5.2

Multiply $x$ by $x$ .

$6 x^{3} - 5 x^{2} - 1 \cdot 6 x^{2} - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.6

Multiply $- 1$ by $6$ .

$6 x^{3} - 5 x^{2} - 6 x^{2} - x \cdot - 5 - 12 (6 x) - 12 \cdot - 5$

Step 4.1.7

Multiply $- 5$ by $- 1$ .

$6 x^{3} - 5 x^{2} - 6 x^{2} + 5 x - 12 (6 x) - 12 \cdot - 5$

Step 4.1.8

Multiply $6$ by $- 12$ .

$6 x^{3} - 5 x^{2} - 6 x^{2} + 5 x - 72 x - 12 \cdot - 5$

Step 4.1.9

Multiply $- 12$ by $- 5$ .

$6 x^{3} - 5 x^{2} - 6 x^{2} + 5 x - 72 x + 60$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Subtract $6 x^{2}$ from $- 5 x^{2}$ .

$6 x^{3} - 11 x^{2} + 5 x - 72 x + 60$

Step 4.2.2

Subtract $72 x$ from $5 x$ .

$6 x^{3} - 11 x^{2} - 67 x + 60$