Basic Math Examples

$3 (m - 1) - 4 {(m - 1)}^{2} + 3 {(m - 1)}^{3}$

Step 1

Factor $m - 1$ out of $3 (m - 1) - 4 {(m - 1)}^{2} + 3 {(m - 1)}^{3}$ .

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Step 1.1

Factor $m - 1$ out of $3 (m - 1)$ .

$(m - 1) \cdot 3 - 4 {(m - 1)}^{2} + 3 {(m - 1)}^{3}$

Step 1.2

Factor $m - 1$ out of $- 4 {(m - 1)}^{2}$ .

$(m - 1) \cdot 3 + (m - 1) (- 4 (m - 1)) + 3 {(m - 1)}^{3}$

Step 1.3

Factor $m - 1$ out of $3 {(m - 1)}^{3}$ .

$(m - 1) \cdot 3 + (m - 1) (- 4 (m - 1)) + (m - 1) (3 {(m - 1)}^{2})$

Step 1.4

Factor $m - 1$ out of $(m - 1) \cdot 3 + (m - 1) (- 4 (m - 1))$ .

$(m - 1) \cdot (3 - 4 (m - 1)) + (m - 1) (3 {(m - 1)}^{2})$

Step 1.5

Factor $m - 1$ out of $(m - 1) \cdot (3 - 4 (m - 1)) + (m - 1) (3 {(m - 1)}^{2})$ .

$(m - 1) (3 - 4 (m - 1) + 3 {(m - 1)}^{2})$

Step 2

Apply the distributive property.

$(m - 1) (3 - 4 m - 4 \cdot - 1 + 3 {(m - 1)}^{2})$

Step 3

Multiply $- 4$ by $- 1$ .

$(m - 1) (3 - 4 m + 4 + 3 {(m - 1)}^{2})$

Step 4

Rewrite ${(m - 1)}^{2}$ as $(m - 1) (m - 1)$ .

$(m - 1) (3 - 4 m + 4 + 3 ((m - 1) (m - 1)))$

Step 5

Expand $(m - 1) (m - 1)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$(m - 1) (3 - 4 m + 4 + 3 (m (m - 1) - 1 (m - 1)))$

Step 5.2

Apply the distributive property.

$(m - 1) (3 - 4 m + 4 + 3 (m \cdot m + m \cdot - 1 - 1 (m - 1)))$

Step 5.3

Apply the distributive property.

$(m - 1) (3 - 4 m + 4 + 3 (m \cdot m + m \cdot - 1 - 1 m - 1 \cdot - 1))$

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

Multiply $m$ by $m$ .

$(m - 1) (3 - 4 m + 4 + 3 (m^{2} + m \cdot - 1 - 1 m - 1 \cdot - 1))$

Step 6.1.2

Move $- 1$ to the left of $m$ .

$(m - 1) (3 - 4 m + 4 + 3 (m^{2} - 1 m - 1 m - 1 \cdot - 1))$

Step 6.1.3

Rewrite $- 1 m$ as $- m$ .

$(m - 1) (3 - 4 m + 4 + 3 (m^{2} - m - 1 m - 1 \cdot - 1))$

Step 6.1.4

Rewrite $- 1 m$ as $- m$ .

$(m - 1) (3 - 4 m + 4 + 3 (m^{2} - m - m - 1 \cdot - 1))$

Step 6.1.5

Multiply $- 1$ by $- 1$ .

$(m - 1) (3 - 4 m + 4 + 3 (m^{2} - m - m + 1))$

Step 6.2

Subtract $m$ from $- m$ .

$(m - 1) (3 - 4 m + 4 + 3 (m^{2} - 2 m + 1))$

Step 7

Apply the distributive property.

$(m - 1) (3 - 4 m + 4 + 3 m^{2} + 3 (- 2 m) + 3 \cdot 1)$

Step 8

Simplify.

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Step 8.1

Multiply $- 2$ by $3$ .

$(m - 1) (3 - 4 m + 4 + 3 m^{2} - 6 m + 3 \cdot 1)$

Step 8.2

Multiply $3$ by $1$ .

$(m - 1) (3 - 4 m + 4 + 3 m^{2} - 6 m + 3)$

Step 9

Add $3$ and $4$ .

$(m - 1) (- 4 m + 7 + 3 m^{2} - 6 m + 3)$

Step 10

Subtract $6 m$ from $- 4 m$ .

$(m - 1) (- 10 m + 7 + 3 m^{2} + 3)$

Step 11

Add $7$ and $3$ .

$(m - 1) (- 10 m + 3 m^{2} + 10)$

Step 12

Reorder terms.

$(m - 1) (3 m^{2} - 10 m + 10)$