Pre-Algebra Examples

(2 c + 3) (2 c - 3)

$(2 c + 3) (2 c - 3)$

Step 1

Expand

(2 c + 3) (2 c - 3)

$(2 c + 3) (2 c - 3)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 c (2 c - 3) + 3 (2 c - 3)

$2 c (2 c - 3) + 3 (2 c - 3)$

Step 1.2

Apply the distributive property.

2 c (2 c) + 2 c \cdot - 3 + 3 (2 c - 3)

$2 c (2 c) + 2 c \cdot - 3 + 3 (2 c - 3)$

Step 1.3

Apply the distributive property.

2 c (2 c) + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3

$2 c (2 c) + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3$

2 c (2 c) + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3

$2 c (2 c) + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3$

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.

2 \cdot 2 c \cdot c + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3

$2 \cdot 2 c \cdot c + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3$

Step 2.1.2

Multiply

c

$c$ by

c

$c$ by adding the exponents.

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Step 2.1.2.1

Move

c

$c$ .

2 \cdot 2 (c \cdot c) + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3

$2 \cdot 2 (c \cdot c) + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3$

Step 2.1.2.2

Multiply

c

$c$ by

c

$c$ .

2 \cdot 2 c^{2} + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3

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

2 \cdot 2 c^{2} + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3

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

Step 2.1.3

Multiply

2

$2$ by

2

$2$ .

4 c^{2} + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3

$4 c^{2} + 2 c \cdot - 3 + 3 (2 c) + 3 \cdot - 3$

Step 2.1.4

Multiply

- 3

$- 3$ by

2

$2$ .

4 c^{2} - 6 c + 3 (2 c) + 3 \cdot - 3

$4 c^{2} - 6 c + 3 (2 c) + 3 \cdot - 3$

Step 2.1.5

Multiply

2

$2$ by

3

$3$ .

4 c^{2} - 6 c + 6 c + 3 \cdot - 3

$4 c^{2} - 6 c + 6 c + 3 \cdot - 3$

Step 2.1.6

Multiply

3

$3$ by

- 3

$- 3$ .

4 c^{2} - 6 c + 6 c - 9

$4 c^{2} - 6 c + 6 c - 9$

4 c^{2} - 6 c + 6 c - 9

$4 c^{2} - 6 c + 6 c - 9$

Step 2.2

Add

- 6 c

$- 6 c$ and

6 c

$6 c$ .

4 c^{2} + 0 - 9

$4 c^{2} + 0 - 9$

Step 2.3

Add

4 c^{2}

$4 c^{2}$ and

0

$0$ .

4 c^{2} - 9

$4 c^{2} - 9$

4 c^{2} - 9

$4 c^{2} - 9$