Precalculus Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

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

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

Step 2.1.4

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

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

Step 2.1.5

Multiply $2 x$ by $1$ .

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

Step 2.1.6

Multiply $- 1$ by $1$ .

$2 x^{2} - x + 2 x - 1$

Step 2.2

Add $- x$ and $2 x$ .

$2 x^{2} + x - 1$