Please forgive this most basic and fundamental of algebra questions but as I enter the calculus arena there is one small algebra function that has eluded intuitive understanding. In factoring quadratics and other polynomials, I am very successfully able to work the operations of factoring but one thing bugs me. I'm a self-educating 64 yo physics student so I have no teacher or colleague to ask.(adsbygoogle = window.adsbygoogle || []).push({});

Where did the middle term come from?

If I factor: 4x^{2}- 28x + 49 I get (2x-7)(2x-7) or (2x-7)^{2}

If I then "FOIL" the terms (2x)(2x)-14x-14x +(-7x)(-7x) I again get 4x^{2}-28x+49

Intuitively, at least for my old brain, (2x-7)^{2}gives 4x^{2}+49

Just writing this down I'm feeling dumb but using this method how or why is the 28x generated from (2x-7)^{2}?

Many thanks and Sorry for the High School question.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Don't Know Much About Al-ge-bra

**Physics Forums | Science Articles, Homework Help, Discussion**