# How do you factor the expression x^2 - 10x + 25?

Apr 22, 2018

x²-10x+25=(x-5)²

#### Explanation:

x²-10x+25

Delta=b²-4ac

Delta=(-10)²-4*1*25

$\Delta = 100 - 100$

$\Delta = 0$

So:

$x = - \frac{b}{2 a}$

$x = \frac{10}{2} = 5$

So :

x²-10x+25=(x-5)²

May 17, 2018

x²-10x+25=(x-5)²

#### Explanation:

x²-10x+25

=x²-5x-5x+25

$= x \left(x - 5\right) - 5 \left(x - 5\right)$

$= \left(x - 5\right) \left(x - 5\right)$

=(x-5)²

Aug 5, 2018

${\left(x - 5\right)}^{2}$

#### Explanation:

To factor this, let's do a little thought experiment:

What two numbers sum up to the middle term ($- 10$) and have a product of the last term ($25$)?

After some trial and error, we arrive at $- 5$ and $- 5$. This means we can factor this as

$\left(x - 5\right) \left(x - 5\right)$, which can be alternatively written as ${\left(x - 5\right)}^{2}$.

Hope this helps!