Basic Math Examples

$- 2 r^{4} s^{5} (6 s^{2} - 7 r + 5)$

Step 1

Apply the distributive property.

$- 2 r^{4} s^{5} (6 s^{2}) - 2 r^{4} s^{5} (- 7 r) - 2 r^{4} s^{5} \cdot 5$

Step 2

Simplify.

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Step 2.1

Multiply $s^{5}$ by $s^{2}$ by adding the exponents.

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Step 2.1.1

Move $s^{2}$ .

$- 2 r^{4} (s^{2} s^{5}) \cdot 6 - 2 r^{4} s^{5} (- 7 r) - 2 r^{4} s^{5} \cdot 5$

Step 2.1.2

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

$- 2 r^{4} s^{2 + 5} \cdot 6 - 2 r^{4} s^{5} (- 7 r) - 2 r^{4} s^{5} \cdot 5$

Step 2.1.3

Add $2$ and $5$ .

$- 2 r^{4} s^{7} \cdot 6 - 2 r^{4} s^{5} (- 7 r) - 2 r^{4} s^{5} \cdot 5$

Step 2.2

Multiply $r^{4}$ by $r$ by adding the exponents.

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Step 2.2.1

Move $r$ .

$- 2 r^{4} s^{7} \cdot 6 - 2 (r \cdot r^{4}) s^{5} \cdot - 7 - 2 r^{4} s^{5} \cdot 5$

Step 2.2.2

Multiply $r$ by $r^{4}$ .

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Step 2.2.2.1

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

$- 2 r^{4} s^{7} \cdot 6 - 2 (r^{1} r^{4}) s^{5} \cdot - 7 - 2 r^{4} s^{5} \cdot 5$

Step 2.2.2.2

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

$- 2 r^{4} s^{7} \cdot 6 - 2 r^{1 + 4} s^{5} \cdot - 7 - 2 r^{4} s^{5} \cdot 5$

Step 2.2.3

Add $1$ and $4$ .

$- 2 r^{4} s^{7} \cdot 6 - 2 r^{5} s^{5} \cdot - 7 - 2 r^{4} s^{5} \cdot 5$

Step 2.3

Multiply $5$ by $- 2$ .

$- 2 r^{4} s^{7} \cdot 6 - 2 r^{5} s^{5} \cdot - 7 - 10 r^{4} s^{5}$

Step 3

Simplify each term.

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Step 3.1

Multiply $6$ by $- 2$ .

$- 12 r^{4} s^{7} - 2 r^{5} s^{5} \cdot - 7 - 10 r^{4} s^{5}$

Step 3.2

Multiply $- 7$ by $- 2$ .

$- 12 r^{4} s^{7} + 14 r^{5} s^{5} - 10 r^{4} s^{5}$