Basic Math Examples

$5 c {(c - 4)}^{2}$

Step 1

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

$5 c ((c - 4) (c - 4))$

Step 2

Expand $(c - 4) (c - 4)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 c (c (c - 4) - 4 (c - 4))$

Step 2.2

Apply the distributive property.

$5 c (c \cdot c + c \cdot - 4 - 4 (c - 4))$

Step 2.3

Apply the distributive property.

$5 c (c \cdot c + c \cdot - 4 - 4 c - 4 \cdot - 4)$

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

Multiply $c$ by $c$ .

$5 c (c^{2} + c \cdot - 4 - 4 c - 4 \cdot - 4)$

Step 3.1.2

Move $- 4$ to the left of $c$ .

$5 c (c^{2} - 4 \cdot c - 4 c - 4 \cdot - 4)$

Step 3.1.3

Multiply $- 4$ by $- 4$ .

$5 c (c^{2} - 4 c - 4 c + 16)$

Step 3.2

Subtract $4 c$ from $- 4 c$ .

$5 c (c^{2} - 8 c + 16)$

Step 4

Apply the distributive property.

$5 c \cdot c^{2} + 5 c (- 8 c) + 5 c \cdot 16$

Step 5

Simplify.

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Step 5.1

Multiply $c$ by $c^{2}$ by adding the exponents.

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Step 5.1.1

Move $c^{2}$ .

$5 (c^{2} c) + 5 c (- 8 c) + 5 c \cdot 16$

Step 5.1.2

Multiply $c^{2}$ by $c$ .

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Step 5.1.2.1

Raise $c$ to the power of $1$ .

$5 (c^{2} c^{1}) + 5 c (- 8 c) + 5 c \cdot 16$

Step 5.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 c^{2 + 1} + 5 c (- 8 c) + 5 c \cdot 16$

Step 5.1.3

Add $2$ and $1$ .

$5 c^{3} + 5 c (- 8 c) + 5 c \cdot 16$

Step 5.2

Rewrite using the commutative property of multiplication.

$5 c^{3} + 5 \cdot - 8 c \cdot c + 5 c \cdot 16$

Step 5.3

Multiply $16$ by $5$ .

$5 c^{3} + 5 \cdot - 8 c \cdot c + 80 c$

Step 6

Simplify each term.

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Step 6.1

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

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Step 6.1.1

Move $c$ .

$5 c^{3} + 5 \cdot - 8 (c \cdot c) + 80 c$

Step 6.1.2

Multiply $c$ by $c$ .

$5 c^{3} + 5 \cdot - 8 c^{2} + 80 c$

Step 6.2

Multiply $5$ by $- 8$ .

$5 c^{3} - 40 c^{2} + 80 c$