# Indices

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#1
Just a couple of basic questions....

I am not sure how they got the extra 1.04 in the second line???

80000 x .04^n-1 = 125000 x 1.04^n - 125000

80000 x 1.04^n-1 = 125000 x 1.04 x 1.04^n-1 -125000

Also different of two squares in this trig question...

cos^4theta - sin^4theta

factorised

(cos^2theta + sin^2theta)(cos^2theta - sin^2theta)

When you expand this wouldnt you be left with cos^4theta - sin^4theta again anyway coz you would at the 2's up?

In the book it says its - cos^2theta - sin^2theta

Just want to make it clear in my head because I thought you added the powers up when you multiply them.... doesn't seem to apply in this case???
0
4 years ago
#2
(Original post by christinajane)
Just a couple of basic questions....

I am not sure how they got the extra 1.04 in the second line???

80000 x .04^n-1 = 125000 x 1.04^n - 125000

80000 x 1.04^n-1 = 125000 x 1.04 x 1.04^n-1 -125000[
We have . Like you said, when you multiply, you add the powers and .

0
4 years ago
#3
(Original post by christinajane)
x
For the first: essentially by definition.
For the second think trig identities.
0
4 years ago
#4
(Original post by christinajane)

Also different of two squares in this trig question...

cos^4theta - sin^4theta

factorised

(cos^2theta + sin^2theta)(cos^2theta - sin^2theta)
Yes, this is correct.

When you expand this wouldnt you be left with cos^4theta - sin^4theta again anyway coz you would at the 2's up?
Of course you'd get again, that's the whole point of factorising, to write something in a factored way, when you expand it, you'd better hope to that you get the same thing again. If not, then something's gone wrong.

If I write then when I expand I had better get again...

in the book it says its - cos^2theta - sin^2theta
We have . Remember that handy little identity in your formula booklet that tells you ?

This means .

Just want to make it clear in my head because I thought you added the powers up when you multiply them.... doesn't seem to apply in this case???
This is always true. (as long as the bases are the same, obviously).
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