Basic Math Examples

10 c^{4} (5 c + 3 c^{7} + 4)

$10 c^{4} (5 c + 3 c^{7} + 4)$

Step 1

Apply the distributive property.

10 c^{4} (5 c) + 10 c^{4} (3 c^{7}) + 10 c^{4} \cdot 4

$10 c^{4} (5 c) + 10 c^{4} (3 c^{7}) + 10 c^{4} \cdot 4$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

10 \cdot 5 c^{4} c + 10 c^{4} (3 c^{7}) + 10 c^{4} \cdot 4

$10 \cdot 5 c^{4} c + 10 c^{4} (3 c^{7}) + 10 c^{4} \cdot 4$

Step 2.2

Rewrite using the commutative property of multiplication.

10 \cdot 5 c^{4} c + 10 \cdot 3 c^{4} c^{7} + 10 c^{4} \cdot 4

$10 \cdot 5 c^{4} c + 10 \cdot 3 c^{4} c^{7} + 10 c^{4} \cdot 4$

Step 2.3

Multiply

4

$4$ by

10

$10$ .

10 \cdot 5 c^{4} c + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$10 \cdot 5 c^{4} c + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

10 \cdot 5 c^{4} c + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$10 \cdot 5 c^{4} c + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

Step 3

Simplify each term.

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Step 3.1

Multiply

c^{4}

$c^{4}$ by

c

$c$ by adding the exponents.

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Step 3.1.1

Move

c

$c$ .

10 \cdot 5 (c \cdot c^{4}) + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$10 \cdot 5 (c \cdot c^{4}) + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

Step 3.1.2

Multiply

c

$c$ by

c^{4}

$c^{4}$ .

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Step 3.1.2.1

Raise

c

$c$ to the power of

1

$1$ .

10 \cdot 5 (c^{1} c^{4}) + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$10 \cdot 5 (c^{1} c^{4}) + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

Step 3.1.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

10 \cdot 5 c^{1 + 4} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$10 \cdot 5 c^{1 + 4} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

10 \cdot 5 c^{1 + 4} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$10 \cdot 5 c^{1 + 4} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

Step 3.1.3

Add

1

$1$ and

4

$4$ .

10 \cdot 5 c^{5} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$10 \cdot 5 c^{5} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

10 \cdot 5 c^{5} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$10 \cdot 5 c^{5} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

Step 3.2

Multiply

10

$10$ by

5

$5$ .

50 c^{5} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}

$50 c^{5} + 10 \cdot 3 c^{4} c^{7} + 40 c^{4}$

Step 3.3

Multiply

c^{4}

$c^{4}$ by

c^{7}

$c^{7}$ by adding the exponents.

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Step 3.3.1

Move

c^{7}

$c^{7}$ .

50 c^{5} + 10 \cdot 3 (c^{7} c^{4}) + 40 c^{4}

$50 c^{5} + 10 \cdot 3 (c^{7} c^{4}) + 40 c^{4}$

Step 3.3.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

50 c^{5} + 10 \cdot 3 c^{7 + 4} + 40 c^{4}

$50 c^{5} + 10 \cdot 3 c^{7 + 4} + 40 c^{4}$

Step 3.3.3

Add

7

$7$ and

4

$4$ .

50 c^{5} + 10 \cdot 3 c^{11} + 40 c^{4}

$50 c^{5} + 10 \cdot 3 c^{11} + 40 c^{4}$

50 c^{5} + 10 \cdot 3 c^{11} + 40 c^{4}

$50 c^{5} + 10 \cdot 3 c^{11} + 40 c^{4}$

Step 3.4

Multiply

10

$10$ by

3

$3$ .

50 c^{5} + 30 c^{11} + 40 c^{4}

$50 c^{5} + 30 c^{11} + 40 c^{4}$

50 c^{5} + 30 c^{11} + 40 c^{4}

$50 c^{5} + 30 c^{11} + 40 c^{4}$

Step 4

Reorder

50 c^{5}

$50 c^{5}$ and

30 c^{11}

$30 c^{11}$ .

30 c^{11} + 50 c^{5} + 40 c^{4}

$30 c^{11} + 50 c^{5} + 40 c^{4}$