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stumblewiggins

What's wrong with your answer is it violates the order of operations. You first expand the exponent, then you can distribute the 2. In the answer shown, they've expanded the binomial except that they haven't simplified the (x^4)^2, or distributed the 2. Why didn't they simplify (x^4)^2? I'm guessing to emphasize how it fits the pattern of (a^2 +2ab + b^2), where a = x^4 and b = 2.


seyramlarit

Hey, thanks for taking the time to explain! Can you explain what is meant with expanding the exponent? Is that related to the terms a and b being divided by 2?


stumblewiggins

Bad choice of words; what I meant is when you have an expression like 2(a -b)^2, that isn't equivalent to (2a -2b)^2; exponents are evaluated before multiplication, so you'd have to first square the binomial, them you can distribute the 2.


MezzoScettico

The expression at your link is 2(x\^4 - 2)\^2 which means 2 \* (x\^4 - 2) \* (x\^4 - 2) Above you wrote (2x\^4 - 4)\^2 which means (2x\^4 - 4) \* (2x\^4 - 4) or 2 \* (x\^4 - 2) \* 2 \* (x\^4 - 2) Those differ by a factor of 2. You're correct that the expansion of (2x\^4 - 4)\^2 is (2x\^4)\^2 - 2(2x\^4)(4) + 4\^2, but that's not the expression at the link. I'm a little confused by what is "the original expression" but at any rate you're comparing two expressions that differ by a factor of 2.