Never fear, eagle's sidekick is
here!
2y^2 - 32 = (2y-8)(y+4)
Will be posting the method shortly
but I have to reserve a spot for my post. =P
This is gonna be a bit hard to
explain...
2y^2 - 32 = 2y^2 + 0y
-32
First you draw an X. There
are four numbers you have to place on each point of the
X.
2y
-8
X
y
4
The two numbers on the left, when
multiplied, must be equal to the the coefficient of y^2 (i.e. The
number next to y^2 in your equation). In this case the coefficient
is 2, and the only two factors of 2 are 1 and 2. Therefore, we
place 2y at the top and 1y below (you can swap them if you want, it
doesn't matter.)
On the right side of the X, you
again have two numbers. These two numbers, when multiplied, must be
equal to the constant, which is in this case -32. There are
multiple possible combinations: you could have 1 and -32, 2 and
-16, 4 and -8 etc. (Note that you can swap the negative symbols
around between the two numbers). The constant is the number in the
equation without a y next to it.
However, this is where it gets
tricky. Multiply the numbers diagonally across the two lines of the
X. In the example of the cross I gave above, I multiply 2y with 4
and y with -8. This results in the numbers 8y and -8y. The two
results you get (in this case 8y and -8y) must be equal to the
middle term. (In this case, notice the middle term is actually 0y.)
Therefore, because 8y and -8y, when added together, = 0y, this
is the correct combination.
After that, simply take the top
two numbers of the cross and place them together in brackets (2y-8)
next to the bottom two numbers, also in brackets (y+4). Your
factorisation is complete. The result is (2y-8)(y+4) =
0.
Since (2y-8)(y+4) = 0, Either
(2y-8) will be equal to 0 OR (y+4) is equal to 0. This is because
for two numbers that are multiplied to be equal to 0, at least
one of them will be 0, because anything multipled by 0 IS
0. For example, 1x0 = 0, 2x0 = 0 and so on.
So, we say that:
2y-8 = 0 OR
y+4=0
2y =
8 OR y = -4
y = 4
Therefore, y has two possible
values: 4 or -4.
Boss eagle, did I do I good job?
Read his answer. I made a stupid
mistake. =(