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.

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# Don't Know Much About Al-ge-bra

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