Basic Math Examples

${(c - 3)}^{2} - (c - 1) (c - 2)$

Step 1

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

$(c - 3) (c - 3) - (c - 1) (c - 2)$

Step 2

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

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Step 2.1

Apply the distributive property.

$c (c - 3) - 3 (c - 3) - (c - 1) (c - 2)$

Step 2.2

Apply the distributive property.

$c \cdot c + c \cdot - 3 - 3 (c - 3) - (c - 1) (c - 2)$

Step 2.3

Apply the distributive property.

$c \cdot c + c \cdot - 3 - 3 c - 3 \cdot - 3 - (c - 1) (c - 2)$

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 $c$ .

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

Step 3.1.2

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

$c^{2} - 3 c - 3 c - 3 \cdot - 3 - (c - 1) (c - 2)$

Step 3.1.3

Multiply $- 3$ by $- 3$ .

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

Step 3.2

Subtract $3 c$ from $- 3 c$ .

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $- 1$ by $- 1$ .

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

Step 6

Expand $(- c + 1) (c - 2)$ using the FOIL Method.

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Step 6.1

Apply the distributive property.

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

Step 6.2

Apply the distributive property.

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

Step 6.3

Apply the distributive property.

$c^{2} - 6 c + 9 - c \cdot c - c \cdot - 2 + 1 c + 1 \cdot - 2$

Step 7

Simplify and combine like terms.

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Step 7.1

Simplify each term.

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Step 7.1.1

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

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Step 7.1.1.1

Move $c$ .

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

Step 7.1.1.2

Multiply $c$ by $c$ .

$c^{2} - 6 c + 9 - c^{2} - c \cdot - 2 + 1 c + 1 \cdot - 2$

Step 7.1.2

Multiply $- 2$ by $- 1$ .

$c^{2} - 6 c + 9 - c^{2} + 2 c + 1 c + 1 \cdot - 2$

Step 7.1.3

Multiply $c$ by $1$ .

$c^{2} - 6 c + 9 - c^{2} + 2 c + c + 1 \cdot - 2$

Step 7.1.4

Multiply $- 2$ by $1$ .

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

Step 7.2

Add $2 c$ and $c$ .

$c^{2} - 6 c + 9 - c^{2} + 3 c - 2$

Step 8

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

$- 6 c + 9 + 0 + 3 c - 2$

Step 9

Add $- 6 c$ and $0$ .

$- 6 c + 9 + 3 c - 2$

Step 10

Add $- 6 c$ and $3 c$ .

$- 3 c + 9 - 2$

Step 11

Subtract $2$ from $9$ .

$- 3 c + 7$

Step 12

Factor $- 1$ out of $- 3 c + 7$ .

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Step 12.1

Factor $- 1$ out of $- 3 c$ .

$- (3 c) + 7$

Step 12.2

Rewrite $7$ as $- 1 (- 7)$ .

$- (3 c) - 1 (- 7)$

Step 12.3

Factor $- 1$ out of $- (3 c) - 1 (- 7)$ .

$- (3 c - 7)$