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Exponents RationalExpressions BoxMethod QuadraticEquations
NumberProperties FractionsinEquations SumandProductPuzzles StandardFormofQuadraticFunction
PropertiesofEquality LinearEquations SolvingInequalities MultiplyingPolynomials item2c
HowtoFindSlope SystemsofEquations FactoringPolynomials item3a
SquareRootsSquareNumbers xandyintercepts FactoringTrinomials item5a
PythagoreanTheorem
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Using the 'Box Method' aka
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One of the easiest methods to help in factoring quadratic equations or in multiplying polynomials is a method that uses a lattice or 'box.' Once you've learned how to use this method, you may never want to go to any other method like FOIL.

Multiplying Polynomials

Here's a common problem found in a math book (we are starting out easy). Going step-by-step, see just how simple it is to use the Box Method which is also known as 'generic rectangles.'

(x  + 5)(x
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Step 1: Make the boxes

Look at your problem. In our problem we have two binomials. This means we need to make a 2x2 box.
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Step 2: Do the Math

Going systematically, starting in the top left corner, begin multiplying!
I like to start at the top left…
 
 
 
 
then move to the top right.
 
 
As I keep working, box-by-box, I continue…
 
 
 
 
until I get to the very last box.
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Step 3: Simplify what's in the Box

Now, all you have to do is take what is in the box and simplify!
  1. Beginning in the TOP left and moving through each box (by going systematically through the boxes I know I won't make any mistakes!), begin simplifying.
  2. Look at the DIAGONAL (see circled terms in pink). These can be simplified.
  3. Continue…

You're done!

-7x + 5x = -2x
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Here…try a few on your own!

(x  + 9)(x

©2011–2014 Sherry Skipper Spurgeon.

All Rights Reserved.

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