Algebra Examples

3 (4 x - 3) (4 x + 3)

$3 (4 x - 3) (4 x + 3)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

(3 (4 x) + 3 \cdot - 3) (4 x + 3)

$(3 (4 x) + 3 \cdot - 3) (4 x + 3)$

Step 1.2

Multiply.

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Step 1.2.1

Multiply

4

$4$ by

3

$3$ .

(12 x + 3 \cdot - 3) (4 x + 3)

$(12 x + 3 \cdot - 3) (4 x + 3)$

Step 1.2.2

Multiply

3

$3$ by

- 3

$- 3$ .

(12 x - 9) (4 x + 3)

$(12 x - 9) (4 x + 3)$

(12 x - 9) (4 x + 3)

$(12 x - 9) (4 x + 3)$

(12 x - 9) (4 x + 3)

$(12 x - 9) (4 x + 3)$

Step 2

Expand

(12 x - 9) (4 x + 3)

$(12 x - 9) (4 x + 3)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

12 x (4 x + 3) - 9 (4 x + 3)

$12 x (4 x + 3) - 9 (4 x + 3)$

Step 2.2

Apply the distributive property.

12 x (4 x) + 12 x \cdot 3 - 9 (4 x + 3)

$12 x (4 x) + 12 x \cdot 3 - 9 (4 x + 3)$

Step 2.3

Apply the distributive property.

12 x (4 x) + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3

$12 x (4 x) + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3$

12 x (4 x) + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3

$12 x (4 x) + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

12 \cdot 4 x \cdot x + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3

$12 \cdot 4 x \cdot x + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3$

Step 3.1.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 3.1.2.1

Move

x

$x$ .

12 \cdot 4 (x \cdot x) + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3

$12 \cdot 4 (x \cdot x) + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3$

Step 3.1.2.2

Multiply

x

$x$ by

x

$x$ .

12 \cdot 4 x^{2} + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3

$12 \cdot 4 x^{2} + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3$

12 \cdot 4 x^{2} + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3

$12 \cdot 4 x^{2} + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3$

Step 3.1.3

Multiply

12

$12$ by

4

$4$ .

48 x^{2} + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3

$48 x^{2} + 12 x \cdot 3 - 9 (4 x) - 9 \cdot 3$

Step 3.1.4

Multiply

3

$3$ by

12

$12$ .

48 x^{2} + 36 x - 9 (4 x) - 9 \cdot 3

$48 x^{2} + 36 x - 9 (4 x) - 9 \cdot 3$

Step 3.1.5

Multiply

4

$4$ by

- 9

$- 9$ .

48 x^{2} + 36 x - 36 x - 9 \cdot 3

$48 x^{2} + 36 x - 36 x - 9 \cdot 3$

Step 3.1.6

Multiply

- 9

$- 9$ by

3

$3$ .

48 x^{2} + 36 x - 36 x - 27

$48 x^{2} + 36 x - 36 x - 27$

48 x^{2} + 36 x - 36 x - 27

$48 x^{2} + 36 x - 36 x - 27$

Step 3.2

Subtract

36 x

$36 x$ from

36 x

$36 x$ .

48 x^{2} + 0 - 27

$48 x^{2} + 0 - 27$

Step 3.3

Add

48 x^{2}

$48 x^{2}$ and

0

$0$ .

48 x^{2} - 27

$48 x^{2} - 27$

48 x^{2} - 27

$48 x^{2} - 27$