Question

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

Answer 1

`(p-7)(p-7)`

Explanation:

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

`(p-7)(p-7)`

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.

Answer 2

See below.

Explanation:

The perfect squares formula is in the form: `(x-a)^2`. Expanding,

`(x-a)^2=x^2-2ax+a^2`

Set this equal to `x^2-14x+49`.

So:

`a^2=49`, or `a=\pm7`

But,

`-2ax=-14x`, so `a=7`.

Thus, `p^2-14p+49=(p-7)^2`.

Or, factor by splitting.

`p^2-7p-7p+49`

`p(p-7)-7(p-7)`

`(p-7)(p-7)`

`=(p-7)^2`