Basic Math Examples

$35 a^{5} b^{5} - 20^{4} b^{4} \cdot (20 a b) - 10 a^{4} b$

Step 1

Factor $a b$ out of $35 a^{5} b^{5} - 20^{4} b^{4} \cdot (20 a b) - 10 a^{4} b$ .

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Step 1.1

Factor $a b$ out of $35 a^{5} b^{5}$ .

$a b (35 a^{4} b^{4}) - 20^{4} b^{4} \cdot (20 a b) - 10 a^{4} b$

Step 1.2

Factor $a b$ out of $- 20^{4} b^{4} \cdot (20 a b)$ .

$a b (35 a^{4} b^{4}) + a b (- 20^{4} b^{3} \cdot (20 b)) - 10 a^{4} b$

Step 1.3

Factor $a b$ out of $- 10 a^{4} b$ .

$a b (35 a^{4} b^{4}) + a b (- 20^{4} b^{3} \cdot (20 b)) + a b (- 10 a^{3})$

Step 1.4

Factor $a b$ out of $a b (35 a^{4} b^{4}) + a b (- 20^{4} b^{3} \cdot (20 b))$ .

$a b (35 a^{4} b^{4} - 20^{4} b^{3} \cdot (20 b)) + a b (- 10 a^{3})$

Step 1.5

Factor $a b$ out of $a b (35 a^{4} b^{4} - 20^{4} b^{3} \cdot (20 b)) + a b (- 10 a^{3})$ .

$a b (35 a^{4} b^{4} - 20^{4} b^{3} \cdot (20 b) - 10 a^{3})$

Step 2

Combine exponents.

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Step 2.1

Multiply $20$ by $- 1$ .

$a b (35 a^{4} b^{4} - 20 \cdot 20^{4} b^{3} \cdot b - 10 a^{3})$

Step 2.2

Factor out negative.

$a b (35 a^{4} b^{4} - (20 \cdot 20^{4}) b^{3} \cdot b - 10 a^{3})$

Step 2.3

Raise $20$ to the power of $1$ .

$a b (35 a^{4} b^{4} - (20^{1} \cdot 20^{4}) b^{3} \cdot b - 10 a^{3})$

Step 2.4

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

$a b (35 a^{4} b^{4} - 20^{1 + 4} b^{3} \cdot b - 10 a^{3})$

Step 2.5

Add $1$ and $4$ .

$a b (35 a^{4} b^{4} - 20^{5} b^{3} \cdot b - 10 a^{3})$

Step 2.6

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

$a b (35 a^{4} b^{4} - 20^{5} (b^{1} b^{3}) - 10 a^{3})$

Step 2.7

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

$a b (35 a^{4} b^{4} - 20^{5} b^{1 + 3} - 10 a^{3})$

Step 2.8

Add $1$ and $3$ .

$a b (35 a^{4} b^{4} - 20^{5} b^{4} - 10 a^{3})$

Step 3

Factor $- 1$ out of $35 a^{4} b^{4} - 20^{5} b^{4} - 10 a^{3}$ .

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Step 3.1

Factor $- 1$ out of $35 a^{4} b^{4}$ .

$a b (- (- 35 a^{4} b^{4}) - 20^{5} b^{4} - 10 a^{3})$

Step 3.2

Factor $- 1$ out of $- 20^{5} b^{4}$ .

$a b (- (- 35 a^{4} b^{4}) - (20^{5} b^{4}) - 10 a^{3})$

Step 3.3

Factor $- 1$ out of $- 10 a^{3}$ .

$a b (- (- 35 a^{4} b^{4}) - (20^{5} b^{4}) - (10 a^{3}))$

Step 3.4

Factor $- 1$ out of $- (- 35 a^{4} b^{4}) - (20^{5} b^{4})$ .

$a b (- (- 35 a^{4} b^{4} + 20^{5} b^{4}) - (10 a^{3}))$

Step 3.5

Factor $- 1$ out of $- (- 35 a^{4} b^{4} + 20^{5} b^{4}) - (10 a^{3})$ .

$a b (- (- 35 a^{4} b^{4} + 20^{5} b^{4} + 10 a^{3}))$

Step 4

Raise $20$ to the power of $5$ .

$a b (- (- 35 a^{4} b^{4} + 3200000 b^{4} + 10 a^{3}))$

Step 5

Factor.

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Step 5.1

Factor $5$ out of $- 35 a^{4} b^{4} + 3200000 b^{4} + 10 a^{3}$ .

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Step 5.1.1

Factor $5$ out of $- 35 a^{4} b^{4}$ .

$a b (- (5 (- 7 a^{4} b^{4}) + 3200000 b^{4} + 10 a^{3}))$

Step 5.1.2

Factor $5$ out of $3200000 b^{4}$ .

$a b (- (5 (- 7 a^{4} b^{4}) + 5 (640000 b^{4}) + 10 a^{3}))$

Step 5.1.3

Factor $5$ out of $10 a^{3}$ .

$a b (- (5 (- 7 a^{4} b^{4}) + 5 (640000 b^{4}) + 5 (2 a^{3})))$

Step 5.1.4

Factor $5$ out of $5 (- 7 a^{4} b^{4}) + 5 (640000 b^{4})$ .

$a b (- (5 (- 7 a^{4} b^{4} + 640000 b^{4}) + 5 (2 a^{3})))$

Step 5.1.5

Factor $5$ out of $5 (- 7 a^{4} b^{4} + 640000 b^{4}) + 5 (2 a^{3})$ .

$a b (- (5 (- 7 a^{4} b^{4} + 640000 b^{4} + 2 a^{3})))$

Step 5.2

Remove unnecessary parentheses.

$a b (- 1 \cdot 5 (- 7 a^{4} b^{4} + 640000 b^{4} + 2 a^{3}))$

Step 6

Factor.

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Step 6.1

Multiply $- 1$ by $5$ .

$a b (- 5 (- 7 a^{4} b^{4} + 640000 b^{4} + 2 a^{3}))$

Step 6.2

Remove unnecessary parentheses.

$a b \cdot - 5 (- 7 a^{4} b^{4} + 640000 b^{4} + 2 a^{3})$

Step 7

Factor.

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Step 7.1

Factor $- 1$ out of $- 7 a^{4} b^{4} + 640000 b^{4} + 2 a^{3}$ .

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Step 7.1.1

Factor $- 1$ out of $- 7 a^{4} b^{4}$ .

$a b \cdot - 5 (- (7 a^{4} b^{4}) + 640000 b^{4} + 2 a^{3})$

Step 7.1.2

Factor $- 1$ out of $640000 b^{4}$ .

$a b \cdot - 5 (- (7 a^{4} b^{4}) - (- 640000 b^{4}) + 2 a^{3})$

Step 7.1.3

Factor $- 1$ out of $2 a^{3}$ .

$a b \cdot - 5 (- (7 a^{4} b^{4}) - (- 640000 b^{4}) - (- 2 a^{3}))$

Step 7.1.4

Factor $- 1$ out of $- (7 a^{4} b^{4}) - (- 640000 b^{4})$ .

$a b \cdot - 5 (- (7 a^{4} b^{4} - 640000 b^{4}) - (- 2 a^{3}))$

Step 7.1.5

Factor $- 1$ out of $- (7 a^{4} b^{4} - 640000 b^{4}) - (- 2 a^{3})$ .

$a b \cdot - 5 (- (7 a^{4} b^{4} - 640000 b^{4} - 2 a^{3}))$

Step 7.2

Remove unnecessary parentheses.

$a b \cdot - 5 \cdot - 1 (7 a^{4} b^{4} - 640000 b^{4} - 2 a^{3})$

Step 8

Combine exponents.

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Step 8.1

Factor out negative.

$- (a b \cdot - 5 (7 a^{4} b^{4} - 640000 b^{4} - 2 a^{3}))$

Step 8.2

Multiply $- 5$ by $- 1$ .

$5 (a b (7 a^{4} b^{4} - 640000 b^{4} - 2 a^{3}))$

Step 9

Remove unnecessary parentheses.

$5 a b (7 a^{4} b^{4} - 640000 b^{4} - 2 a^{3})$