Basic Math Examples

$((8 m^{2} + 4 m - 7) - (2 m^{2} - 5 m + 2)) (m^{2} + m + 1)$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$(8 m^{2} + 4 m - 7 - (2 m^{2}) - (- 5 m) - 1 \cdot 2) (m^{2} + m + 1)$

Step 1.1.2

Simplify.

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Step 1.1.2.1

Multiply $2$ by $- 1$ .

$(8 m^{2} + 4 m - 7 - 2 m^{2} - (- 5 m) - 1 \cdot 2) (m^{2} + m + 1)$

Step 1.1.2.2

Multiply $- 5$ by $- 1$ .

$(8 m^{2} + 4 m - 7 - 2 m^{2} + 5 m - 1 \cdot 2) (m^{2} + m + 1)$

Step 1.1.2.3

Multiply $- 1$ by $2$ .

$(8 m^{2} + 4 m - 7 - 2 m^{2} + 5 m - 2) (m^{2} + m + 1)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $2 m^{2}$ from $8 m^{2}$ .

$(6 m^{2} + 4 m - 7 + 5 m - 2) (m^{2} + m + 1)$

Step 1.2.2

Add $4 m$ and $5 m$ .

$(6 m^{2} + 9 m - 7 - 2) (m^{2} + m + 1)$

Step 1.2.3

Subtract $2$ from $- 7$ .

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

Step 2

Expand $(6 m^{2} + 9 m - 9) (m^{2} + m + 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

Move $m^{2}$ .

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

Step 3.1.1.2

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

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

Step 3.1.1.3

Add $2$ and $2$ .

$6 m^{4} + 6 m^{2} m + 6 m^{2} \cdot 1 + 9 m \cdot m^{2} + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.2

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

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Step 3.1.2.1

Move $m$ .

$6 m^{4} + 6 (m \cdot m^{2}) + 6 m^{2} \cdot 1 + 9 m \cdot m^{2} + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.2.2

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

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Step 3.1.2.2.1

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

$6 m^{4} + 6 (m^{1} m^{2}) + 6 m^{2} \cdot 1 + 9 m \cdot m^{2} + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.2.2.2

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

$6 m^{4} + 6 m^{1 + 2} + 6 m^{2} \cdot 1 + 9 m \cdot m^{2} + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.2.3

Add $1$ and $2$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} \cdot 1 + 9 m \cdot m^{2} + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.3

Multiply $6$ by $1$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m \cdot m^{2} + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.4

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

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Step 3.1.4.1

Move $m^{2}$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 (m^{2} m) + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.4.2

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

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Step 3.1.4.2.1

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

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 (m^{2} m^{1}) + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.4.2.2

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

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{2 + 1} + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.4.3

Add $2$ and $1$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 m \cdot m + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.5

Multiply $m$ by $m$ by adding the exponents.

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Step 3.1.5.1

Move $m$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 (m \cdot m) + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.5.2

Multiply $m$ by $m$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 m^{2} + 9 m \cdot 1 - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.6

Multiply $9$ by $1$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 m^{2} + 9 m - 9 m^{2} - 9 m - 9 \cdot 1$

Step 3.1.7

Multiply $- 9$ by $1$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 m^{2} + 9 m - 9 m^{2} - 9 m - 9$

Step 3.2

Simplify by adding terms.

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Step 3.2.1

Combine the opposite terms in $6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 m^{2} + 9 m - 9 m^{2} - 9 m - 9$ .

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Step 3.2.1.1

Subtract $9 m^{2}$ from $9 m^{2}$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 m + 0 - 9 m - 9$

Step 3.2.1.2

Add $6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 m$ and $0$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 9 m - 9 m - 9$

Step 3.2.1.3

Subtract $9 m$ from $9 m$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} + 0 - 9$

Step 3.2.1.4

Add $6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3}$ and $0$ .

$6 m^{4} + 6 m^{3} + 6 m^{2} + 9 m^{3} - 9$

Step 3.2.2

Add $6 m^{3}$ and $9 m^{3}$ .

$6 m^{4} + 15 m^{3} + 6 m^{2} - 9$