Basic Math Examples

${(c + 3)}^{2} (c - 8) (c - 1) = 16$

Step 1

Simplify ${(c + 3)}^{2} (c - 8) (c - 1)$ .

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Step 1.1

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

$(c + 3) (c + 3) (c - 8) (c - 1) = 16$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$(c (c + 3) + 3 (c + 3)) (c - 8) (c - 1) = 16$

Step 1.2.2

Apply the distributive property.

$(c \cdot c + c \cdot 3 + 3 (c + 3)) (c - 8) (c - 1) = 16$

Step 1.2.3

Apply the distributive property.

$(c \cdot c + c \cdot 3 + 3 c + 3 \cdot 3) (c - 8) (c - 1) = 16$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $c$ by $c$ .

$(c^{2} + c \cdot 3 + 3 c + 3 \cdot 3) (c - 8) (c - 1) = 16$

Step 1.3.1.2

Move $3$ to the left of $c$ .

$(c^{2} + 3 \cdot c + 3 c + 3 \cdot 3) (c - 8) (c - 1) = 16$

Step 1.3.1.3

Multiply $3$ by $3$ .

$(c^{2} + 3 c + 3 c + 9) (c - 8) (c - 1) = 16$

Step 1.3.2

Add $3 c$ and $3 c$ .

$(c^{2} + 6 c + 9) (c - 8) (c - 1) = 16$

Step 1.4

Expand $(c^{2} + 6 c + 9) (c - 8)$ by multiplying each term in the first expression by each term in the second expression.

$(c^{2} c + c^{2} \cdot - 8 + 6 c \cdot c + 6 c \cdot - 8 + 9 c + 9 \cdot - 8) (c - 1) = 16$

Step 1.5

Simplify terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

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

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Step 1.5.1.1.1

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

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Step 1.5.1.1.1.1

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

$(c^{2} c^{1} + c^{2} \cdot - 8 + 6 c \cdot c + 6 c \cdot - 8 + 9 c + 9 \cdot - 8) (c - 1) = 16$

Step 1.5.1.1.1.2

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

$(c^{2 + 1} + c^{2} \cdot - 8 + 6 c \cdot c + 6 c \cdot - 8 + 9 c + 9 \cdot - 8) (c - 1) = 16$

Step 1.5.1.1.2

Add $2$ and $1$ .

$(c^{3} + c^{2} \cdot - 8 + 6 c \cdot c + 6 c \cdot - 8 + 9 c + 9 \cdot - 8) (c - 1) = 16$

Step 1.5.1.2

Move $- 8$ to the left of $c^{2}$ .

$(c^{3} - 8 \cdot c^{2} + 6 c \cdot c + 6 c \cdot - 8 + 9 c + 9 \cdot - 8) (c - 1) = 16$

Step 1.5.1.3

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

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Step 1.5.1.3.1

Move $c$ .

$(c^{3} - 8 c^{2} + 6 (c \cdot c) + 6 c \cdot - 8 + 9 c + 9 \cdot - 8) (c - 1) = 16$

Step 1.5.1.3.2

Multiply $c$ by $c$ .

$(c^{3} - 8 c^{2} + 6 c^{2} + 6 c \cdot - 8 + 9 c + 9 \cdot - 8) (c - 1) = 16$

Step 1.5.1.4

Multiply $- 8$ by $6$ .

$(c^{3} - 8 c^{2} + 6 c^{2} - 48 c + 9 c + 9 \cdot - 8) (c - 1) = 16$

Step 1.5.1.5

Multiply $9$ by $- 8$ .

$(c^{3} - 8 c^{2} + 6 c^{2} - 48 c + 9 c - 72) (c - 1) = 16$

Step 1.5.2

Simplify by adding terms.

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Step 1.5.2.1

Add $- 8 c^{2}$ and $6 c^{2}$ .

$(c^{3} - 2 c^{2} - 48 c + 9 c - 72) (c - 1) = 16$

Step 1.5.2.2

Add $- 48 c$ and $9 c$ .

$(c^{3} - 2 c^{2} - 39 c - 72) (c - 1) = 16$

Step 1.6

Expand $(c^{3} - 2 c^{2} - 39 c - 72) (c - 1)$ by multiplying each term in the first expression by each term in the second expression.

$c^{3} c + c^{3} \cdot - 1 - 2 c^{2} c - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7

Simplify terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

Multiply $c^{3}$ by $c$ by adding the exponents.

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Step 1.7.1.1.1

Multiply $c^{3}$ by $c$ .

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Step 1.7.1.1.1.1

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

$c^{3} c^{1} + c^{3} \cdot - 1 - 2 c^{2} c - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.1.1.2

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

$c^{3 + 1} + c^{3} \cdot - 1 - 2 c^{2} c - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.1.2

Add $3$ and $1$ .

$c^{4} + c^{3} \cdot - 1 - 2 c^{2} c - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.2

Move $- 1$ to the left of $c^{3}$ .

$c^{4} - 1 \cdot c^{3} - 2 c^{2} c - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.3

Rewrite $- 1 c^{3}$ as $- c^{3}$ .

$c^{4} - c^{3} - 2 c^{2} c - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.4

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

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Step 1.7.1.4.1

Move $c$ .

$c^{4} - c^{3} - 2 (c \cdot c^{2}) - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.4.2

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

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Step 1.7.1.4.2.1

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

$c^{4} - c^{3} - 2 (c^{1} c^{2}) - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.4.2.2

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

$c^{4} - c^{3} - 2 c^{1 + 2} - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.4.3

Add $1$ and $2$ .

$c^{4} - c^{3} - 2 c^{3} - 2 c^{2} \cdot - 1 - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.5

Multiply $- 1$ by $- 2$ .

$c^{4} - c^{3} - 2 c^{3} + 2 c^{2} - 39 c \cdot c - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.6

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

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Step 1.7.1.6.1

Move $c$ .

$c^{4} - c^{3} - 2 c^{3} + 2 c^{2} - 39 (c \cdot c) - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.6.2

Multiply $c$ by $c$ .

$c^{4} - c^{3} - 2 c^{3} + 2 c^{2} - 39 c^{2} - 39 c \cdot - 1 - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.7

Multiply $- 1$ by $- 39$ .

$c^{4} - c^{3} - 2 c^{3} + 2 c^{2} - 39 c^{2} + 39 c - 72 c - 72 \cdot - 1 = 16$

Step 1.7.1.8

Multiply $- 72$ by $- 1$ .

$c^{4} - c^{3} - 2 c^{3} + 2 c^{2} - 39 c^{2} + 39 c - 72 c + 72 = 16$

Step 1.7.2

Simplify by adding terms.

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Step 1.7.2.1

Subtract $2 c^{3}$ from $- c^{3}$ .

$c^{4} - 3 c^{3} + 2 c^{2} - 39 c^{2} + 39 c - 72 c + 72 = 16$

Step 1.7.2.2

Subtract $39 c^{2}$ from $2 c^{2}$ .

$c^{4} - 3 c^{3} - 37 c^{2} + 39 c - 72 c + 72 = 16$

Step 1.7.2.3

Subtract $72 c$ from $39 c$ .

$c^{4} - 3 c^{3} - 37 c^{2} - 33 c + 72 = 16$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$c \approx - 3.5516382, - 2.31610764, 0.84897032, 8.01877551$

Step 3