# explain factoring quadratic equations by grouping to me like I'm an idiot **URL:** \ **Category:** Factual Questions\ **Created:** [September 6, 2010, 8:27pm UTC](https://boards.straightdope.com/t/explain-factoring-quadratic-equations-by-grouping-to-me-like-im-an-idiot/552834 "2010-09-06T20:27:13Z")\ **Posts on this page:** 6\ **Page:** 2
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [May 21, 2015, 5:19pm UTC](https://boards.straightdope.com/t/explain-factoring-quadratic-equations-by-grouping-to-me-like-im-an-idiot/552834/21 "2015-05-21T17:19:01Z")
> [@The\_Tao\_s\_Revenge](#): > > I get it! > > That is basically an abstract version of how we all did multiplication by hand in the third grade. It’s not the vulcan mental calisthenics it appeared to be. It finally clicked. > > Via the distributive property we can prove 4²-2² = (4-2)(4+2) > > (4-2)(4+2) > > 4² + 4_2 + -2_4 + -(2²) > > Which simplifies to > 4²-2² > So to surmise: > > (x-y)(x+y) = x² + xy + -xy + -(y²) = x²-y² > > I think I’m getting it! > > Thanks everyone! All your posts really are helping. My head feels about like a square peg after a journey through a round hole, but that’ll pass. I had the same feeling after learning subnetting. > > Also **friedo** , sorry about the reality altering typo. > > I’m gonna get some sleep and come back and reread things. Thanks again! Incidentally in a week or two they will teach you the quadratic formula which takes all of the guess work out of factoring quadratics, and makes much of this moot. But they want to teach you this way first so you can get a feel for what the quadratic formula is doing. Sort of like teaching you to calculate 4\*3 as 4+4+4 before they each you the multiplication table. ---
**Author:** ![Flander](https://avatars.discourse-cdn.com/v4/letter/f/8c91f0/32.png) [@Flander](https://boards.straightdope.com/u/Flander)\ **Post date:** [May 21, 2015, 5:51pm UTC](https://boards.straightdope.com/t/explain-factoring-quadratic-equations-by-grouping-to-me-like-im-an-idiot/552834/22 "2015-05-21T17:51:14Z")
> [@Buck\_Godot](#): > > Incidentally\*\* in a week or two\*\* they will teach you the quadratic formula which takes all of the guess work out of factoring quadratics, and makes much of this moot. But they want to teach you this way first so you can get a feel for what the quadratic formula is doing. Sort of like teaching you to calculate 4\*3 as 4+4+4 before they each you the multiplication table. _bolding mine_ Finally! After 5 years of intermediate algebra, they will teach him the quadratic formula. :smack: ---
**Author:** ![Your\_Great\_Darsh\_Face](https://avatars.discourse-cdn.com/v4/letter/y/ac8455/32.png) [@Your\_Great\_Darsh\_Face](https://boards.straightdope.com/u/Your_Great_Darsh_Face)\ **Post date:** [May 21, 2015, 5:54pm UTC](https://boards.straightdope.com/t/explain-factoring-quadratic-equations-by-grouping-to-me-like-im-an-idiot/552834/23 "2015-05-21T17:54:53Z")
> [@Buck\_Godot](#): > > Incidentally in a week or two they will teach you the quadratic formula which takes all of the guess work out of factoring quadratics, and makes much of this moot. But they want to teach you this way first so you can get a feel for what the quadratic formula is doing. Sort of like teaching you to calculate 4\*3 as 4+4+4 before they each you the multiplication table. Incidentally, if you can factorise a quadratic without recourse to the formula, it is often a lot less work to do so. If there is any doubt then you can check the discriminant b[sup]2[/sup] - 4ac and if this is a perfect square then the quadratic has integer factors. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 21, 2015, 9:43pm UTC](https://boards.straightdope.com/t/explain-factoring-quadratic-equations-by-grouping-to-me-like-im-an-idiot/552834/24 "2015-05-21T21:43:06Z")
Well, rational factors, at least. And it’s only “often” less work to do, if by that you mean “for the sorts of problems one is likely to encounter in an algebra textbook”. Across the entire universe of possible problems, it is far more often the case that the quadratic formula is the easiest method, even when other methods can be used. Now add in that the other methods can’t always be used, even in textbook problems. Overall, I would generally advise that if you can’t see the solution within ten or twenty seconds, just go ahead and use the quadratic formula. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [May 21, 2015, 10:15pm UTC](https://boards.straightdope.com/t/explain-factoring-quadratic-equations-by-grouping-to-me-like-im-an-idiot/552834/25 "2015-05-21T22:15:06Z")
> [@Chronos](#): > > Well, rational factors, at least. Right; for example, consider 4x^2 - 1 = 0. Here, b^2 - 4ac = 4, a perfect square, but the roots are non-integers. What we can say is that b^2 - 4ac is a perfect square if and only if ax^2 + bx + c can be factored into (integer coefficient) polynomials of degree \<= 1. [Proof: being worked on by **Chronos** in the other thread. :)] ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [May 21, 2015, 10:21pm UTC](https://boards.straightdope.com/t/explain-factoring-quadratic-equations-by-grouping-to-me-like-im-an-idiot/552834/26 "2015-05-21T22:21:40Z")
Oh, I see now **Your Great Darsh Face** was discussing “integer factors”, not “integer roots”. Thus, **Your Great Darsh Face** was perfectly correct, **Chronos** ’s replacement with “rational” was a miscorrection, and my post was largely pointless. Sorry! :smack: [Previous page](https://boards.straightdope.com/t/explain-factoring-quadratic-equations-by-grouping-to-me-like-im-an-idiot/552834.md?page=1)