Question

I have a number of problems I'm having problem with but they start with the example given in the book

2x^2 - 10x
=2(x^2 - 5x)
=2{[x-(5/2)]^2 - [(5/2)^2]}
=2[x-(5/2)]^2 - (25/2)

Why isn't (5/2)^2 (25/4)?

I'm struggling with the exercises as well.

3x^2 - 24x
I get 3(x-4)^2 - 16 or if I try to follow the example, 3(x-4)^2 - 32, but the answer at the back of the book is 3(x-4)^2 - 48

Answer 1

I meant, "Why isn't (25/2)^2 (25/4)?"

Answer 2

You seem to have forgotten a basic rule of multiplying fractions.

a/b * c/d = ac/(bd)

The square of any fraction a/b is a^2/b^2.

For example, 2/3 of 2/3 = (2/3)^2 = 4/9
and (25/2)^2 = 625/4

Looking at your second problem,
3x^2 - 24x
= 3(x^2 -8x) Now add and subtract 48
= 3(x^2 -8x +16) -48
= 3(x-4)^2 -48