Binomial Expansion

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We can use the binomial theorem to expand and simplify expressions of the form where n is any positive whole number.

The general expansions is

Example:

We evaluate the coefficient of each power of and simplify:

Example:

which simplifies to

then

Suppose we have an expansion. We know and but not n. If we have a relationship between the coefficients we may be able to form an equation to find n. Suppose in the expansion below we know that the coefficient of equals the coefficient of

The coefficient of is

The coefficient of is

Equate these: Now cancel where possible

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