Is it 2x² or 4x or 4x²?
please explain why if you can
please explain why if you can
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Just because some of the answers are wrong (which is really sad, actually...), I wanted to say that the answer is definitely (2x)*(2x) = (2*2)*(x*x) = 4*(x^2), where "x^2" is read as "x squared". I've added lots of parentheses to make sure I'm clear. If you don't believe me (and since some of these answers are wrong I wouldn't really blame you), look at my link, where I had a computer do it.
The technical reason is that multiplication is associative and commutative in the polynomial ring over the reals.... The less technical reason is that, for instance, (3*4)*5 = 3*(4*5), and that this remains true even if you replace 3, 4, and 5 with other numbers. Replacing 3 by 2, 4 by x, and 5 by (2*x), this becomes
(2*x)*(2*x) = 2*(x*(2*x))
Also, 6*7 = 7*6, and this remains true when 6 and 7 are replaced by other numbers. Replacing 6 with x and 7 with (2*x), the above becomes
2*(x*(2*x)) = 2*((2*x)*x)
We can apply the (3*4)*5 = 3*(4*5) style law above but in reverse to this expression to get
2*((2*x)*x) = (2*(2*x))*x
We can apply that same law to the expression 2*(2*x) inside to get
(2*(2*x))*x = ((2*2)*x)*x
Since 2*2 = 4, we have
(4*x)*x
Applying the (3*4)*5 = 3*(4*5) style law one more time, we get
4*(x*x)
By definition, x*x is x squared, which is written as x^2 (or x² as you typed it, though using the ^ symbol is easier). Going through the chain of equalities, we've very rigorously shown that
(2*x)*(2*x) = 4*(x^2).
This is usually written more sloppily as 4x^2.
The technical reason is that multiplication is associative and commutative in the polynomial ring over the reals.... The less technical reason is that, for instance, (3*4)*5 = 3*(4*5), and that this remains true even if you replace 3, 4, and 5 with other numbers. Replacing 3 by 2, 4 by x, and 5 by (2*x), this becomes
(2*x)*(2*x) = 2*(x*(2*x))
Also, 6*7 = 7*6, and this remains true when 6 and 7 are replaced by other numbers. Replacing 6 with x and 7 with (2*x), the above becomes
2*(x*(2*x)) = 2*((2*x)*x)
We can apply the (3*4)*5 = 3*(4*5) style law above but in reverse to this expression to get
2*((2*x)*x) = (2*(2*x))*x
We can apply that same law to the expression 2*(2*x) inside to get
(2*(2*x))*x = ((2*2)*x)*x
Since 2*2 = 4, we have
(4*x)*x
Applying the (3*4)*5 = 3*(4*5) style law one more time, we get
4*(x*x)
By definition, x*x is x squared, which is written as x^2 (or x² as you typed it, though using the ^ symbol is easier). Going through the chain of equalities, we've very rigorously shown that
(2*x)*(2*x) = 4*(x^2).
This is usually written more sloppily as 4x^2.
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It's basic. 2x times 2x is 2x^2. I learned this is algebra earlier this year. Right now, since X isn't defined, it doesn't effect the 2. So look at it as 2 times 2 then add the X. So it's 2^2 then 2X^2. Makes it easier to understand.
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2x squared.
Think of it like other non-X problems
5 times 5 = 5 squared. Etc.
Think of it like other non-X problems
5 times 5 = 5 squared. Etc.
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it is 4x squared, because 2 times 2 is 4 and x times x is x squared
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2 times 2 = 4......
2x times 2x = 4x²
{}
2x times 2x = 4x²
{}
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2 times 2 = 4
x times x = x²
Therefore... 4x²
x times x = x²
Therefore... 4x²
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4x squared (sorry dont know how to put exponents)
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It is in fact 4x^2. Here's a check. Insert 3 for x. 2(3)*2(3)=6*6=36. 4(3^2)=4(9)=36
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it is (2x)^2 = 4x^2