Addition and Subtraction of Like Terms
- Thread starter Norloonda
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mmm4444bot
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The Order of Operations tells us that multiplication happens before addition.
We're not adding up the a's separately and then adding up the b's because a and b are multiplied together first.
We're adding up products ab.
4ab means four of them added together: ab+ab+ab+ab
2ab means two of them added together: ab+ab
When we combine 4ab+2ab, we end up with six of them added together: ab+ab+ab+ab+ab+ab.
We write that as 6ab. :cool:
Steven G
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ab is a number which we do not know the value of and may never know the value of.
Consider x + x which equals 2x. This is true regardless of what x equals. Another words 7+7 = 2*7. 9+9 = 2*9. 2/3 + 2/3 =2*(2/3). It does not matter what x equals!
Now 4x+2x = 6x. After all 4x = x+x+x+x and 2x=x+x, so 4x+2x= x+x+x+x + x+x = 6x. But a better way to see this is you have 4x's and someone gives you 2 more x's so you have 6x's. Think of x say as a five dollar bill. 4-$5 + 2-$5 = 4*5 + 2*5 = 6*5
Now ab is a number just like x is a number. Think of ab as 4*3 or 12. Well 4-12s + 2-12s = 5-12s. Realize that the 12s can be replaced with ANY number. Like 4-9s + 2-9s = 6-9s. So 4-ab + 2-ab = 6ab, ie 4*ab + 2*ab = 6ab