Re-arranging a formula

How do I re-arrange the following to get the answer?

y = a(x-p)(x-q), where x = (p+q)/2

THE ANSWER:
y = ((ap-aq)(q-p))/2

I will give best answer. :)

y = a ( x - p ) ( x - q ), where x = ( p + q ) / 2

Substituting x:

y = a ( [ ( p + q ) / 2 ] - p ) ( [ ( p + q ) / 2 ] - q )

Subtracting the like terms the in both halves:

y = a [ ( q - p ) / 2 ] [ ( p - q ) / 2 ]

Taking out the 1/2 since it's a common factor:

y = a [ ( q - p ) ( p - q ) ] / 2

And if you apply distributive to the second half:

y = [ ( q - p ) ( ap - aq ) ] / 2 <<<<------ :D The answer, problem solved.

Haha, good luck getting that answer past your teacher!

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x - p = (q - p)/2
x - q = (p - q)/2
So y = a(x - p)(x - q) = -a(p - q)²/4.

@Daaa :) You don't take out common factors when you're multiplying!