Finite Math Examples

$m^{2} - 49 c^{2} + 42 c - 9$

Step 1

Regroup terms.

$m^{2} - 49 c^{2} + 42 c - 9$

Step 2

Factor $- 1$ out of $- 49 c^{2} + 42 c - 9$ .

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Step 2.1

Factor $- 1$ out of $- 49 c^{2}$ .

$m^{2} - (49 c^{2}) + 42 c - 9$

Step 2.2

Factor $- 1$ out of $42 c$ .

$m^{2} - (49 c^{2}) - (- 42 c) - 9$

Step 2.3

Rewrite $- 9$ as $- 1 (9)$ .

$m^{2} - (49 c^{2}) - (- 42 c) - 1 (9)$

Step 2.4

Factor $- 1$ out of $- (49 c^{2}) - (- 42 c)$ .

$m^{2} - (49 c^{2} - 42 c) - 1 (9)$

Step 2.5

Factor $- 1$ out of $- (49 c^{2} - 42 c) - 1 (9)$ .

$m^{2} - (49 c^{2} - 42 c + 9)$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $49 c^{2}$ as ${(7 c)}^{2}$ .

$m^{2} - ({(7 c)}^{2} - 42 c + 9)$

Step 3.2

Rewrite $9$ as $3^{2}$ .

$m^{2} - ({(7 c)}^{2} - 42 c + 3^{2})$

Step 3.3

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

$42 c = 2 \cdot (7 c) \cdot 3$

Step 3.4

Rewrite the polynomial.

$m^{2} - ({(7 c)}^{2} - 2 \cdot (7 c) \cdot 3 + 3^{2})$

Step 3.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 7 c$ and $b = 3$ .

$m^{2} - {(7 c - 3)}^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 7 c - 3$ .

$(m + 7 c - 3) (m - (7 c - 3))$

Step 5

Simplify.

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Step 5.1

Apply the distributive property.

$(m + 7 c - 3) (m - (7 c) - - 3)$

Step 5.2

Multiply $7$ by $- 1$ .

$(m + 7 c - 3) (m - 7 c - - 3)$

Step 5.3

Multiply $- 1$ by $- 3$ .

$(m + 7 c - 3) (m - 7 c + 3)$