Divide (25m^2-20m+4)÷(5m-2)

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

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.

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

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

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

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

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

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

Rewrite the polynomial.

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

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 $5 m - 2$ .

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$5 m - 2$