Factor 4a^2-20a+25

$4 a^{2} - 20 a + 25$

Step 1

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

${(2 a)}^{2} - 20 a + 25$

Step 2

Rewrite $25$ as $5^{2}$ .

${(2 a)}^{2} - 20 a + 5^{2}$

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

${(2 a - 5)}^{2}$