Algebra Examples

$4 c d - 25 c^{2} - 0.16 d^{2}$

Step 1

Add parentheses.

$4 (c d) - 25 c^{2} - 0.16 d^{2}$

Step 2

Let $u = c d$ . Substitute $u$ for all occurrences of $c d$ .

$4 u - 25 c^{2} - 0.16 d^{2}$

Step 3

Factor $- 1$ out of $4 u - 25 c^{2} - 0.16 d^{2}$ .

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Step 3.1

Move $4 u$ .

$- 25 c^{2} - 0.16 d^{2} + 4 u$

Step 3.2

Factor $- 1$ out of $- 25 c^{2}$ .

$- (25 c^{2}) - 0.16 d^{2} + 4 u$

Step 3.3

Factor $- 1$ out of $- 0.16 d^{2}$ .

$- (25 c^{2}) - (0.16 d^{2}) + 4 u$

Step 3.4

Factor $- 1$ out of $4 u$ .

$- (25 c^{2}) - (0.16 d^{2}) - (- 4 u)$

Step 3.5

Factor $- 1$ out of $- (25 c^{2}) - (0.16 d^{2})$ .

$- (25 c^{2} + 0.16 d^{2}) - (- 4 u)$

Step 3.6

Factor $- 1$ out of $- (25 c^{2} + 0.16 d^{2}) - (- 4 u)$ .

$- (25 c^{2} + 0.16 d^{2} - 4 u)$

Step 4

Factor.

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Step 4.1

Factor $0.04$ out of $25 c^{2} + 0.16 d^{2} - 4 u$ .

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Step 4.1.1

Factor $0.04$ out of $25 c^{2}$ .

$- (0.04 (625 c^{2}) + 0.16 d^{2} - 4 u)$

Step 4.1.2

Factor $0.04$ out of $0.16 d^{2}$ .

$- (0.04 (625 c^{2}) + 0.04 (4 d^{2}) - 4 u)$

Step 4.1.3

Factor $0.04$ out of $- 4 u$ .

$- (0.04 (625 c^{2}) + 0.04 (4 d^{2}) + 0.04 (- 100 u))$

Step 4.1.4

Factor $0.04$ out of $0.04 (625 c^{2}) + 0.04 (4 d^{2})$ .

$- (0.04 (625 c^{2} + 4 d^{2}) + 0.04 (- 100 u))$

Step 4.1.5

Factor $0.04$ out of $0.04 (625 c^{2} + 4 d^{2}) + 0.04 (- 100 u)$ .

$- (0.04 (625 c^{2} + 4 d^{2} - 100 u))$

Step 4.2

Remove unnecessary parentheses.

$- 1 \cdot 0.04 (625 c^{2} + 4 d^{2} - 100 u)$

Step 5

Multiply $- 1$ by $0.04$ .

$- 0.04 (625 c^{2} + 4 d^{2} - 100 u)$

Step 6

Replace all occurrences of $u$ with $c d$ .

$- 0.04 (625 c^{2} + 4 d^{2} - 100 (c d))$

Step 7

Remove parentheses.

$- 0.04 (625 c^{2} + 4 d^{2} - 100 c d)$

Step 8

Factor using the perfect square rule.

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Step 8.1

Rearrange terms.

$- 0.04 (625 c^{2} - 100 c d + 4 d^{2})$

Step 8.2

Rewrite $625 c^{2}$ as ${(25 c)}^{2}$ .

$- 0.04 ({(25 c)}^{2} - 100 c d + 4 d^{2})$

Step 8.3

Rewrite $4 d^{2}$ as ${(2 d)}^{2}$ .

$- 0.04 ({(25 c)}^{2} - 100 c d + {(2 d)}^{2})$

Step 8.4

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$100 c d = 2 \cdot (25 c) \cdot (2 d)$

Step 8.5

Rewrite the polynomial.

$- 0.04 ({(25 c)}^{2} - 2 \cdot (25 c) \cdot (2 d) + {(2 d)}^{2})$

Step 8.6

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 25 c$ and $b = 2 d$ .

$- 0.04 {(25 c - 2 d)}^{2}$