Precalculus Examples

$(2 x + 1) (3 x - 2) - 5 (4 x - 1)$

Step 1

Simplify each term.

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Step 1.1

Expand $(2 x + 1) (3 x - 2)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$2 x (3 x - 2) + 1 (3 x - 2) - 5 (4 x - 1)$

Step 1.1.2

Apply the distributive property.

$2 x (3 x) + 2 x \cdot - 2 + 1 (3 x - 2) - 5 (4 x - 1)$

Step 1.1.3

Apply the distributive property.

$2 x (3 x) + 2 x \cdot - 2 + 1 (3 x) + 1 \cdot - 2 - 5 (4 x - 1)$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x \cdot - 2 + 1 (3 x) + 1 \cdot - 2 - 5 (4 x - 1)$

Step 1.2.1.2

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

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Step 1.2.1.2.1

Move $x$ .

$2 \cdot 3 (x \cdot x) + 2 x \cdot - 2 + 1 (3 x) + 1 \cdot - 2 - 5 (4 x - 1)$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} + 2 x \cdot - 2 + 1 (3 x) + 1 \cdot - 2 - 5 (4 x - 1)$

Step 1.2.1.3

Multiply $2$ by $3$ .

$6 x^{2} + 2 x \cdot - 2 + 1 (3 x) + 1 \cdot - 2 - 5 (4 x - 1)$

Step 1.2.1.4

Multiply $- 2$ by $2$ .

$6 x^{2} - 4 x + 1 (3 x) + 1 \cdot - 2 - 5 (4 x - 1)$

Step 1.2.1.5

Multiply $3 x$ by $1$ .

$6 x^{2} - 4 x + 3 x + 1 \cdot - 2 - 5 (4 x - 1)$

Step 1.2.1.6

Multiply $- 2$ by $1$ .

$6 x^{2} - 4 x + 3 x - 2 - 5 (4 x - 1)$

Step 1.2.2

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

$6 x^{2} - x - 2 - 5 (4 x - 1)$

Step 1.3

Apply the distributive property.

$6 x^{2} - x - 2 - 5 (4 x) - 5 \cdot - 1$

Step 1.4

Multiply $4$ by $- 5$ .

$6 x^{2} - x - 2 - 20 x - 5 \cdot - 1$

Step 1.5

Multiply $- 5$ by $- 1$ .

$6 x^{2} - x - 2 - 20 x + 5$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $20 x$ from $- x$ .

$6 x^{2} - 21 x - 2 + 5$

Step 2.2

Add $- 2$ and $5$ .

$6 x^{2} - 21 x + 3$