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Exercise 2 requires us
to expand and simplify

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the following sets of brackets.

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In order to do this,

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we'll need to multiply each term
in the second bracket by x, <i>et cetera</i> .

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And then each term in the second
bracket by –1, <i>et cetera</i>.

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So x multiplied by the second bracket

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and then –1 multiplied
by the second bracket.

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So expanding these brackets out.

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In the first bracket,
we have x to the power of 1

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multiplied by x to the power of n-1,
x to the power of n-2, <i>et cetera</i>.

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When multiplying terms with the same
base, we know we can add the powers.

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So x to the power of 1
times x to the power of n-1

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leaves us with x to the power of 1
plus n-1, which is n.

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Similarly, x to the 1
times x to the n-2

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leaves us with x to the n-1.

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The next term would give us
x to the n-2, <i>et cetera</i>,

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down to x cubed ...

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... x squared

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and x.

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Then multiplying
the second bracket by –1

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simply makes each term negative,
so we get -x to the n-1,

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-x to the n-2 ... minus ...<i>et cetera</i>,

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-x squared -x –1.

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And so now we've expanded,
we need to try to simplify.

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And we can see there are
a number of like terms.

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So we have +x to the power of n-1

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and then -x to the power of n-1,
which will cancel out.

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Similarly, +x to the n-2,
-x to the n-2.

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+x cubed, and there would be
a -x cubed here.

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+x squared, -x squared.

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+x, -x.

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And once we're done with
all the cancelling,

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all that we're
actually left with

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is the first and last term
of the expansion.

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So expanding out these brackets

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leaves us simply with
x to the power of n-1.