Basic Math Examples

c^{2} - 10 c + 25

$c^{2} - 10 c + 25$

Step 1

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

c^{2} - 10 c + 5^{2}

$c^{2} - 10 c + 5^{2}$

Step 2

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

10 c = 2 \cdot c \cdot 5

$10 c = 2 \cdot c \cdot 5$

Step 3

Rewrite the polynomial.

c^{2} - 2 \cdot c \cdot 5 + 5^{2}

$c^{2} - 2 \cdot c \cdot 5 + 5^{2}$

Step 4

Factor using the perfect square trinomial rule

a^{2} - 2 a b + b^{2} = {(a - b)}^{2}

$a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where

a = c

$a = c$ and

b = 5

$b = 5$ .

{(c - 5)}^{2}

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