Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Apply the distributive property.

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

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

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

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Step 1.2.1.1.1

Move $x$ .

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

Step 1.2.1.1.2

Multiply $x$ by $x$ .

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

Step 1.2.1.2

Multiply $2$ by $3$ .

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

Step 1.2.1.3

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

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

Step 1.2.1.4

Multiply $- 1$ by $2$ .

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

Step 1.2.2

Subtract $x$ from $6 x$ .

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

Step 1.3

Raise $5$ to the power of $2$ .

$3 x^{2} + 5 x - 2 - (2 x + 25)$

Step 1.4

Apply the distributive property.

$3 x^{2} + 5 x - 2 - (2 x) - 1 \cdot 25$

Step 1.5

Multiply $2$ by $- 1$ .

$3 x^{2} + 5 x - 2 - 2 x - 1 \cdot 25$

Step 1.6

Multiply $- 1$ by $25$ .

$3 x^{2} + 5 x - 2 - 2 x - 25$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x$ from $5 x$ .

$3 x^{2} + 3 x - 2 - 25$

Step 2.2

Subtract $25$ from $- 2$ .

$3 x^{2} + 3 x - 27$