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where does the 24xy come from in (6x-2y)^2

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2 Answers

(6x-2y)2 = (6x-2y)(6x-2y)

When you mulitply 2 binomials like this you are doing the distributive property, but you have to distrubute  BOTH the 6x and the -2y.

The shortcut you hear everyone talk about is FOIL(First, Outside, Inside, Last), but it really is distribution.

First: multiply the first terms together (6x)(6x) = 36x2

Outside: multiply the "outside pair" together (6x)(-2y) = -12xy     That was 6x from first binomial and -2y from the second binomial

Inside: multiply the "inside pair" together (-2y)(6x) = -12xy That was -2y from first binomial and 6x from the second binomial

Last: multiply the last terms together (-2y)(-2y)= 4y2

Add all the answers together: 36x2-12xy-12xy+4y2   Combine the xy terms because they are like terms

This simplifies to 36x2-24xy+4y2

Whenever you square a binomial your answer will be 1st term squared + 2(product of the 2 terms) + last term squared.

Walter,

  Jason has given  you the important part of the answer:  FOIL!  Always use this for expanding (multiplying) polynomials that have been simplified into expressions within paranthesises.

BruceS

Note:  The 27 in (6x-2y)2 = (6x-2y)(6x-27) is a typo.

Comments

Thanks Bruce. I just caught my typo and corrected it.

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