Pre-Algebra Examples

${(4 c + 3)}^{2}$

Step 1

Rewrite ${(4 c + 3)}^{2}$ as $(4 c + 3) (4 c + 3)$ .

$(4 c + 3) (4 c + 3)$

Step 2

Expand $(4 c + 3) (4 c + 3)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$4 c (4 c + 3) + 3 (4 c + 3)$

Step 2.2

Apply the distributive property.

$4 c (4 c) + 4 c \cdot 3 + 3 (4 c + 3)$

Step 2.3

Apply the distributive property.

$4 c (4 c) + 4 c \cdot 3 + 3 (4 c) + 3 \cdot 3$

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.

$4 \cdot 4 c \cdot c + 4 c \cdot 3 + 3 (4 c) + 3 \cdot 3$

Step 3.1.2

Multiply $c$ by $c$ by adding the exponents.

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Step 3.1.2.1

Move $c$ .

$4 \cdot 4 (c \cdot c) + 4 c \cdot 3 + 3 (4 c) + 3 \cdot 3$

Step 3.1.2.2

Multiply $c$ by $c$ .

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

Step 3.1.3

Multiply $4$ by $4$ .

$16 c^{2} + 4 c \cdot 3 + 3 (4 c) + 3 \cdot 3$

Step 3.1.4

Multiply $3$ by $4$ .

$16 c^{2} + 12 c + 3 (4 c) + 3 \cdot 3$

Step 3.1.5

Multiply $4$ by $3$ .

$16 c^{2} + 12 c + 12 c + 3 \cdot 3$

Step 3.1.6

Multiply $3$ by $3$ .

$16 c^{2} + 12 c + 12 c + 9$

Step 3.2

Add $12 c$ and $12 c$ .

$16 c^{2} + 24 c + 9$