Algebra Examples

$(2 x + 3) (x - 6) - 2 x^{2} + 3 x + 30$

Step 1

Simplify each term.

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Step 1.1

Expand $(2 x + 3) (x - 6)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$2 x (x - 6) + 3 (x - 6) - 2 x^{2} + 3 x + 30$

Step 1.1.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 6 + 3 (x - 6) - 2 x^{2} + 3 x + 30$

Step 1.1.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 6 + 3 x + 3 \cdot - 6 - 2 x^{2} + 3 x + 30$

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 $x$ .

$2 (x \cdot x) + 2 x \cdot - 6 + 3 x + 3 \cdot - 6 - 2 x^{2} + 3 x + 30$

Step 1.2.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 6 + 3 x + 3 \cdot - 6 - 2 x^{2} + 3 x + 30$

Step 1.2.1.2

Multiply $- 6$ by $2$ .

$2 x^{2} - 12 x + 3 x + 3 \cdot - 6 - 2 x^{2} + 3 x + 30$

Step 1.2.1.3

Multiply $3$ by $- 6$ .

$2 x^{2} - 12 x + 3 x - 18 - 2 x^{2} + 3 x + 30$

Step 1.2.2

Add $- 12 x$ and $3 x$ .

$2 x^{2} - 9 x - 18 - 2 x^{2} + 3 x + 30$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $2 x^{2} - 9 x - 18 - 2 x^{2} + 3 x + 30$ .

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Step 2.1.1

Subtract $2 x^{2}$ from $2 x^{2}$ .

$- 9 x - 18 + 0 + 3 x + 30$

Step 2.1.2

Add $- 9 x - 18$ and $0$ .

$- 9 x - 18 + 3 x + 30$

Step 2.2

Add $- 9 x$ and $3 x$ .

$- 6 x - 18 + 30$

Step 2.3

Add $- 18$ and $30$ .

$- 6 x + 12$