Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 \cdot 7 + 7 (5 m) + {(m + 6)}^{4}$

Step 1.2

Multiply $7$ by $7$ .

$49 + 7 (5 m) + {(m + 6)}^{4}$

Step 1.3

Multiply $5$ by $7$ .

$49 + 35 m + {(m + 6)}^{4}$

Step 1.4

Use the Binomial Theorem.

$49 + 35 m + m^{4} + 4 m^{3} \cdot 6 + 6 m^{2} \cdot 6^{2} + 4 m \cdot 6^{3} + 6^{4}$

Step 1.5

Simplify each term.

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Step 1.5.1

Multiply $6$ by $4$ .

$49 + 35 m + m^{4} + 24 m^{3} + 6 m^{2} \cdot 6^{2} + 4 m \cdot 6^{3} + 6^{4}$

Step 1.5.2

Multiply $6$ by $6^{2}$ by adding the exponents.

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Step 1.5.2.1

Move $6^{2}$ .

$49 + 35 m + m^{4} + 24 m^{3} + 6^{2} \cdot 6 m^{2} + 4 m \cdot 6^{3} + 6^{4}$

Step 1.5.2.2

Multiply $6^{2}$ by $6$ .

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Step 1.5.2.2.1

Raise $6$ to the power of $1$ .

$49 + 35 m + m^{4} + 24 m^{3} + 6^{2} \cdot 6^{1} m^{2} + 4 m \cdot 6^{3} + 6^{4}$

Step 1.5.2.2.2

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

$49 + 35 m + m^{4} + 24 m^{3} + 6^{2 + 1} m^{2} + 4 m \cdot 6^{3} + 6^{4}$

Step 1.5.2.3

Add $2$ and $1$ .

$49 + 35 m + m^{4} + 24 m^{3} + 6^{3} m^{2} + 4 m \cdot 6^{3} + 6^{4}$

Step 1.5.3

Raise $6$ to the power of $3$ .

$49 + 35 m + m^{4} + 24 m^{3} + 216 m^{2} + 4 m \cdot 6^{3} + 6^{4}$

Step 1.5.4

Raise $6$ to the power of $3$ .

$49 + 35 m + m^{4} + 24 m^{3} + 216 m^{2} + 4 m \cdot 216 + 6^{4}$

Step 1.5.5

Multiply $216$ by $4$ .

$49 + 35 m + m^{4} + 24 m^{3} + 216 m^{2} + 864 m + 6^{4}$

Step 1.5.6

Raise $6$ to the power of $4$ .

$49 + 35 m + m^{4} + 24 m^{3} + 216 m^{2} + 864 m + 1296$

Step 2

Simplify by adding terms.

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Step 2.1

Add $49$ and $1296$ .

$35 m + m^{4} + 24 m^{3} + 216 m^{2} + 864 m + 1345$

Step 2.2

Add $35 m$ and $864 m$ .

$m^{4} + 24 m^{3} + 216 m^{2} + 899 m + 1345$