Algebra Examples

$6 u^{2} \cdot {(2 u - 5)}^{2} - 12 u^{2} \cdot (2 u - 5) \cdot (u + 5)$

Step 1

Factor $6 u^{2} (2 u - 5)$ out of $6 u^{2} \cdot {(2 u - 5)}^{2} - 12 u^{2} \cdot (2 u - 5) \cdot (u + 5)$ .

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Step 1.1

Factor $6 u^{2} (2 u - 5)$ out of $6 u^{2} \cdot {(2 u - 5)}^{2}$ .

$6 u^{2} (2 u - 5) (2 u - 5) - 12 u^{2} \cdot (2 u - 5) \cdot (u + 5)$

Step 1.2

Factor $6 u^{2} (2 u - 5)$ out of $- 12 u^{2} \cdot (2 u - 5) \cdot (u + 5)$ .

$6 u^{2} (2 u - 5) (2 u - 5) + 6 u^{2} (2 u - 5) ((- 2) \cdot (u + 5))$

Step 1.3

Factor $6 u^{2} (2 u - 5)$ out of $6 u^{2} (2 u - 5) (2 u - 5) + 6 u^{2} (2 u - 5) ((- 2) \cdot (u + 5))$ .

$6 u^{2} (2 u - 5) (2 u - 5 + (- 2) \cdot (u + 5))$

$6 u^{2} (2 u - 5) (2 u - 5 + (- 2) (u + 5))$

Step 2

Apply the distributive property.

$6 u^{2} (2 u - 5) (2 u - 5 - 2 u - 2 \cdot 5)$

Step 3

Multiply $- 2$ by $5$ .

$6 u^{2} (2 u - 5) (2 u - 5 - 2 u - 10)$

Step 4

Subtract $2 u$ from $2 u$ .

$6 u^{2} (2 u - 5) (0 - 5 - 10)$

Step 5

Subtract $5$ from $0$ .

$6 u^{2} (2 u - 5) (- 5 - 10)$

Step 6

Subtract $10$ from $- 5$ .

$6 u^{2} (2 u - 5) \cdot - 15$

Step 7

Multiply $- 15$ by $6$ .

$- 90 u^{2} (2 u - 5)$