Addition and Subtraction of Binomials, Trinomials, etc.: why is 4xy+2xy=6xy, not 6x^2

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Norloonda

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In combining like terms. Remembering ( x = 1x ).

1. 4xy + 2xy = 6xy. Can anybody explain to me why the answer is 6xy and not 6x2y or any combinations letters used for variables? In short, why can't the ONE (1) for (y) be added also?
 
Norloonda said:
In combining like terms. Remembering ( x = 1x ).

1. 4xy + 2xy = 6xy. Can anybody explain to me why the answer is 6xy and not 6x2y or any combinations letters used for variables? In short, why can't the ONE (1) for (y) be added also?
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You have four xy's and another 2 xy's. You add them to get six xy's. You're not multiplying x's, such as (4x)(2xy) = (4)(2)(x)(x)(y) = 8x^2y.

If you like, you can say that you've got four (1x)(1y)'s, plus another two (1x)(1y)'s, which you're adding to get six (1x)(1y)'s, or 6(1x)(1y) = 6xy. ;)
 
Essentially, it all boils down to the fact that you don't have separate x terms and y terms. Rather, you only have xy terms. I think it might be easier to see using real values. Let's say x = 2 and y = 3 and re-examine the given equation.

4xy + 2xy = 6xy --> 4(2)(3) + 2(2)(3) = 6(2)(3)

I see your question as asking: 'I've got four "2" terms and two more "2" terms, so I've got 6. And I've got one "3" term and one more "3" term so I've got 2.' But that's not really what's going on here. You don't actually have any "2" terms or "3" terms. Instead, you only have "6" (2*3) terms. And you have four "6" terms plus two "6" terms, so you have a total of "6" terms.
 
Norloonda said:
In combining like terms. Remembering ( x = 1x ).

1. 4xy + 2xy = 6xy. Can anybody explain to me why the answer is 6xy and not 6x2y or any combinations letters used for variables? In short, why can't the ONE (1) for (y) be added also?
Click to expand...
xy IS a number, but you don't know what it equals yet and my never know, BUT it is a number. If you had four fives (think 5 dollars bills) and I gave you two fives, you would have six fives (maybe you'd have 4 5's in your left hand and 2 5's in your right hand.

7*2 + 9*2 (same as 7 2's + 9 2's) is 16*2

11*6 + 3*6 = 14*6

98*3 + 2*3 = 100*3 = 300 (no calculator need for this one!)


3xyz + 4xyz = 7xyz
Convince yourself of this. if x=2, y=3 and z=4, then xyz=24

3xyz+ 4xyz = 3*24 + 4*24 = 72 + 96 =168 and 7xyz=7*24=168. So 3xyz + 4xyz and 7xyz are both equal to one another.
 
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