Algebra Examples

$(25 m^{2} - 20 m + 4) \div (5 m - 2)$

Step 1

Rewrite the division as a fraction.

$\frac{25 m^{2} - 20 m + 4}{5 m - 2}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $25 m^{2}$ as ${(5 m)}^{2}$ .

$\frac{{(5 m)}^{2} - 20 m + 4}{5 m - 2}$

Step 2.2

Rewrite $4$ as $2^{2}$ .

$\frac{{(5 m)}^{2} - 20 m + 2^{2}}{5 m - 2}$

Step 2.3

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

$20 m = 2 \cdot (5 m) \cdot 2$

Step 2.4

Rewrite the polynomial.

$\frac{{(5 m)}^{2} - 2 \cdot (5 m) \cdot 2 + 2^{2}}{5 m - 2}$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 m$ and $b = 2$ .

$\frac{{(5 m - 2)}^{2}}{5 m - 2}$

Step 3

Cancel the common factor of ${(5 m - 2)}^{2}$ and $5 m - 2$ .

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Step 3.1

Factor $5 m - 2$ out of ${(5 m - 2)}^{2}$ .

$\frac{(5 m - 2) (5 m - 2)}{5 m - 2}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{(5 m - 2) (5 m - 2)}{(5 m - 2) \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{(5 m - 2) (5 m - 2)}{(5 m - 2) \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{5 m - 2}{1}$

Step 3.2.4

Divide $5 m - 2$ by $1$ .

$5 m - 2$