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

Apr 19, 2018

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

#### Explanation:

Given: ${x}^{2} - 10 x + 25$

Split the middle term.

$= {x}^{2} - 5 x - 5 x + 25$

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

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

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

Apr 19, 2018

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

#### Explanation:

Find what multiplies to give $25$ and adds/subtracts to make $- 10$.

$25$ and $1$ make $25$ but do not add together to make $- 10$.

$5 \text{ and } 5$ add to make $10$ and multiply to make $25$ to make $- 10$ and $25$, the you can multiply and add $- 5$ and $- 5$

Because:

$- \text{ x } - = +$