How do you simpify/expand (2-(x/2))^2?

Question

Wolfram Alpha says the answer is x^2/4 - 4, but I got the polar opposite, 4 - x^2/4 .  Can you show me step by step how you would arrive to get x^2/4 - 4? I won't have Wolfram Alpha on a test, so I any help onto where I might have gone wrong would be greatly appreciated.

Thanks :-)

V. Singh · Accepted Answer

[ 2 - (x/2) ] ^2     this is in the form of  ( A - B )^2  = A^2 - 2AB + B^2, where A = 2 and B = x/2

[ 2 - (x/2) ] ^2 = 2^2 - 2*2*(x/2) + (x/2)^2
                    = 4 - 2x + x^2/4
                    = (x^2)/4 - 2x + 4
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Remember (a + b)^2 = a^2 + 2ab + b^2     and
................ (a - b)^2  = a^2  - 2ab + b^2

hope this helped

Vick

JOS J · Answer

4 - 2 x + x^2/4

Edward · Answer

Impossible The answer should be x^2/4-2x+4
Step1 write (2-x/2)*(2-x/2)
step2 multiply 2 then -x/2 like this: 2*(2-x/2)-x/2*(2-x/2)
equal 4-2x/2-2x/2+x^2/4 note that -x/2*-x/2 makes positive x^2/4
final answer by add the two -2x/2-2x/2 and dividing the 2 gives
4-2x-x^2/4 which u can write in any order

Ian H · Answer

(a - b)^2 = (a - b)(a - b) = a^2 - 2ab + b^2
If a = 2, b = x/2
you get THREE terms
Two of them are  x^2/4  and + 4
That should be enough help for you to finish this


Regards - Ian

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How do you simpify/expand (2-(x/2))^2?

4 Answers