# How do you factor p^2-14p+49 using the perfect squares formula?

Apr 15, 2017

$\left(p - 7\right) \left(p - 7\right)$

#### Explanation:

49 is ${7}^{2}$ so we need to make -14p and +49; therefore both signs in the brackets must minus.

$\left(p - 7\right) \left(p - 7\right)$

Tip; The perfect square formula can be a bit confusing. Just use your intuition if you know the answer. That is what I do and I do not get penalised for it. Just use the formula if necessary.

Apr 15, 2017

See below.

#### Explanation:

The perfect squares formula is in the form: ${\left(x - a\right)}^{2}$. Expanding,

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

Set this equal to ${x}^{2} - 14 x + 49$.

So:

${a}^{2} = 49$, or $a = \setminus \pm 7$

But,

$- 2 a x = - 14 x$, so $a = 7$.

Thus, ${p}^{2} - 14 p + 49 = {\left(p - 7\right)}^{2}$.

Or, factor by splitting.

${p}^{2} - 7 p - 7 p + 49$

$p \left(p - 7\right) - 7 \left(p - 7\right)$

$\left(p - 7\right) \left(p - 7\right)$

$= {\left(p - 7\right)}^{2}$