Hi, can someone please solve this

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

Answer: [ (ap-aq)(q-p) ] / 2

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.

It looks like you are trying to find y in terms of a, p and q which is not quite the same as 'solving' the equation. To do this you need to substitute each x in the second equation with the value of x in terms of p and q

Since x = (p+q)/2
and y = a(x-p)(x-q)

a([(p+q)/2]-p)([(p+q)/2]-q) <== this was literally copy and paste with brackets added for clarity

and simplify the subtraction terms (p+q - 2p)/2 = (q-p)/2 and (p+q-2q)/2 = (p-q)/2
a[(q-p)/2 * (p-q)/2]
[ (ap-aq)(q-p) ] / 4 <== note: don't forget to multiply denominators

looks like it's already solved. haha