Algebra Examples

$3 x (x - 3) + (2 x + 6) (- x - 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 3 + (2 x + 6) (- x - 3)$

Step 1.2

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

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Step 1.2.1

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 3 + (2 x + 6) (- x - 3)$

Step 1.2.2

Multiply $x$ by $x$ .

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

Step 1.3

Multiply $- 3$ by $3$ .

$3 x^{2} - 9 x + (2 x + 6) (- x - 3)$

Step 1.4

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

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Step 1.4.1

Apply the distributive property.

$3 x^{2} - 9 x + 2 x (- x - 3) + 6 (- x - 3)$

Step 1.4.2

Apply the distributive property.

$3 x^{2} - 9 x + 2 x (- x) + 2 x \cdot - 3 + 6 (- x - 3)$

Step 1.4.3

Apply the distributive property.

$3 x^{2} - 9 x + 2 x (- x) + 2 x \cdot - 3 + 6 (- x) + 6 \cdot - 3$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Rewrite using the commutative property of multiplication.

$3 x^{2} - 9 x + 2 \cdot - 1 x \cdot x + 2 x \cdot - 3 + 6 (- x) + 6 \cdot - 3$

Step 1.5.1.2

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

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Step 1.5.1.2.1

Move $x$ .

$3 x^{2} - 9 x + 2 \cdot - 1 (x \cdot x) + 2 x \cdot - 3 + 6 (- x) + 6 \cdot - 3$

Step 1.5.1.2.2

Multiply $x$ by $x$ .

$3 x^{2} - 9 x + 2 \cdot - 1 x^{2} + 2 x \cdot - 3 + 6 (- x) + 6 \cdot - 3$

Step 1.5.1.3

Multiply $2$ by $- 1$ .

$3 x^{2} - 9 x - 2 x^{2} + 2 x \cdot - 3 + 6 (- x) + 6 \cdot - 3$

Step 1.5.1.4

Multiply $- 3$ by $2$ .

$3 x^{2} - 9 x - 2 x^{2} - 6 x + 6 (- x) + 6 \cdot - 3$

Step 1.5.1.5

Multiply $- 1$ by $6$ .

$3 x^{2} - 9 x - 2 x^{2} - 6 x - 6 x + 6 \cdot - 3$

Step 1.5.1.6

Multiply $6$ by $- 3$ .

$3 x^{2} - 9 x - 2 x^{2} - 6 x - 6 x - 18$

Step 1.5.2

Subtract $6 x$ from $- 6 x$ .

$3 x^{2} - 9 x - 2 x^{2} - 12 x - 18$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{2}$ from $3 x^{2}$ .

$x^{2} - 9 x - 12 x - 18$

Step 2.2

Subtract $12 x$ from $- 9 x$ .

$x^{2} - 21 x - 18$