Basic Math Examples

$- 25 c (10 d - 15 d c) - \frac{7^{2} c^{3} d^{4}}{c^{2} d^{3}}$

Step 1

Apply the distributive property.

$- 25 c (10 d) - 25 c (- 15 d c) - \frac{7^{2} c^{3} d^{4}}{c^{2} d^{3}}$

Step 2

Rewrite using the commutative property of multiplication.

$- 25 \cdot 10 c d - 25 c (- 15 d c) - \frac{7^{2} c^{3} d^{4}}{c^{2} d^{3}}$

Step 3

Multiply $c$ by $c$ by adding the exponents.

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Step 3.1

Move $c$ .

$- 25 \cdot 10 c d - 25 (c \cdot c) (- 15 d) - \frac{7^{2} c^{3} d^{4}}{c^{2} d^{3}}$

Step 3.2

Multiply $c$ by $c$ .

$- 25 \cdot 10 c d - 25 c^{2} (- 15 d) - \frac{7^{2} c^{3} d^{4}}{c^{2} d^{3}}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 25$ by $10$ .

$- 250 c d - 25 c^{2} (- 15 d) - \frac{7^{2} c^{3} d^{4}}{c^{2} d^{3}}$

Step 4.2

Rewrite using the commutative property of multiplication.

$- 250 c d - 25 \cdot - 15 c^{2} d - \frac{7^{2} c^{3} d^{4}}{c^{2} d^{3}}$

Step 4.3

Multiply $- 25$ by $- 15$ .

$- 250 c d + 375 c^{2} d - \frac{7^{2} c^{3} d^{4}}{c^{2} d^{3}}$

Step 5

Cancel the common factor of $c^{3}$ and $c^{2}$ .

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Step 5.1

Factor $c^{2}$ out of $7^{2} c^{3} d^{4}$ .

$- 250 c d + 375 c^{2} d - \frac{c^{2} (7^{2} c d^{4})}{c^{2} d^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $c^{2}$ out of $c^{2} d^{3}$ .

$- 250 c d + 375 c^{2} d - \frac{c^{2} (7^{2} c d^{4})}{c^{2} (d^{3})}$

Step 5.2.2

Cancel the common factor.

$- 250 c d + 375 c^{2} d - \frac{c^{2} (7^{2} c d^{4})}{c^{2} d^{3}}$

Step 5.2.3

Rewrite the expression.

$- 250 c d + 375 c^{2} d - \frac{7^{2} c d^{4}}{d^{3}}$

Step 6

Cancel the common factor of $d^{4}$ and $d^{3}$ .

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Step 6.1

Factor $d^{3}$ out of $7^{2} c d^{4}$ .

$- 250 c d + 375 c^{2} d - \frac{d^{3} (7^{2} c d)}{d^{3}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Multiply by $1$ .

$- 250 c d + 375 c^{2} d - \frac{d^{3} (7^{2} c d)}{d^{3} \cdot 1}$

Step 6.2.2

Cancel the common factor.

$- 250 c d + 375 c^{2} d - \frac{d^{3} (7^{2} c d)}{d^{3} \cdot 1}$

Step 6.2.3

Rewrite the expression.

$- 250 c d + 375 c^{2} d - \frac{7^{2} c d}{1}$

Step 6.2.4

Divide $7^{2} c d$ by $1$ .

$- 250 c d + 375 c^{2} d - (7^{2} c d)$

Step 7

Raise $7$ to the power of $2$ .

$- 250 c d + 375 c^{2} d - (49 c d)$

Step 8

Multiply $49$ by $- 1$ .

$- 250 c d + 375 c^{2} d - 49 (c d)$

Step 9

Remove parentheses.

$- 250 c d + 375 c^{2} d - 49 c d$

Step 10

Subtract $49 c d$ from $- 250 c d$ .

$- 299 c d + 375 c^{2} d$

Step 11

Factor $- c d$ out of $- 299 c d + 375 c^{2} d$ .

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Step 11.1

Reorder $- 299 c d$ and $375 c^{2} d$ .

$375 c^{2} d - 299 c d$

Step 11.2

Factor $- c d$ out of $375 c^{2} d$ .

$- c d (- 375 c) - 299 c d$

Step 11.3

Factor $- c d$ out of $- 299 c d$ .

$- c d (- 375 c) - c d (299)$

Step 11.4

Factor $- c d$ out of $- c d (- 375 c) - c d (299)$ .

$- c d (- 375 c + 299)$

Step 12

Factor.

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Step 12.1

Factor $- 1$ out of $- 375 c + 299$ .

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Step 12.1.1

Factor $- 1$ out of $- 375 c$ .

$- c d (- (375 c) + 299)$

Step 12.1.2

Rewrite $299$ as $- 1 (- 299)$ .

$- c d (- (375 c) - 1 (- 299))$

Step 12.1.3

Factor $- 1$ out of $- (375 c) - 1 (- 299)$ .

$- c d (- (375 c - 299))$

Step 12.2

Remove unnecessary parentheses.

$- c d \cdot - 1 (375 c - 299)$

Step 13

Combine exponents.

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Step 13.1

Factor out negative.

$- (c d \cdot - 1 (375 c - 299))$

Step 13.2

Multiply $- 1$ by $- 1$ .

$1 (c d (375 c - 299))$

Step 13.3

Multiply $c$ by $1$ .

$c (d (375 c - 299))$

Step 14

Remove unnecessary parentheses.

$c d (375 c - 299)$