Algebra Examples

(3 x + 7) (3 x - 7)

$(3 x + 7) (3 x - 7)$

Step 1

Expand

(3 x + 7) (3 x - 7)

$(3 x + 7) (3 x - 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

3 x (3 x - 7) + 7 (3 x - 7)

$3 x (3 x - 7) + 7 (3 x - 7)$

Step 1.2

Apply the distributive property.

3 x (3 x) + 3 x \cdot - 7 + 7 (3 x - 7)

$3 x (3 x) + 3 x \cdot - 7 + 7 (3 x - 7)$

Step 1.3

Apply the distributive property.

3 x (3 x) + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7

$3 x (3 x) + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7$

3 x (3 x) + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7

$3 x (3 x) + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7$

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.

3 \cdot 3 x \cdot x + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7

$3 \cdot 3 x \cdot x + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7$

Step 2.1.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.1.2.1

Move

x

$x$ .

3 \cdot 3 (x \cdot x) + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7

$3 \cdot 3 (x \cdot x) + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7$

Step 2.1.2.2

Multiply

x

$x$ by

x

$x$ .

3 \cdot 3 x^{2} + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7

$3 \cdot 3 x^{2} + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7$

3 \cdot 3 x^{2} + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7

$3 \cdot 3 x^{2} + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7$

Step 2.1.3

Multiply

3

$3$ by

3

$3$ .

9 x^{2} + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7

$9 x^{2} + 3 x \cdot - 7 + 7 (3 x) + 7 \cdot - 7$

Step 2.1.4

Multiply

- 7

$- 7$ by

3

$3$ .

9 x^{2} - 21 x + 7 (3 x) + 7 \cdot - 7

$9 x^{2} - 21 x + 7 (3 x) + 7 \cdot - 7$

Step 2.1.5

Multiply

3

$3$ by

7

$7$ .

9 x^{2} - 21 x + 21 x + 7 \cdot - 7

$9 x^{2} - 21 x + 21 x + 7 \cdot - 7$

Step 2.1.6

Multiply

7

$7$ by

- 7

$- 7$ .

9 x^{2} - 21 x + 21 x - 49

$9 x^{2} - 21 x + 21 x - 49$

9 x^{2} - 21 x + 21 x - 49

$9 x^{2} - 21 x + 21 x - 49$

Step 2.2

Add

- 21 x

$- 21 x$ and

21 x

$21 x$ .

9 x^{2} + 0 - 49

$9 x^{2} + 0 - 49$

Step 2.3

Add

9 x^{2}

$9 x^{2}$ and

0

$0$ .

9 x^{2} - 49

$9 x^{2} - 49$

9 x^{2} - 49

$9 x^{2} - 49$