# Binomial theorem

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##### Examples
###### Lessons
1. Expand ${\left( {a + b} \right)^4}$, using:
1. Pascal's Triangle
2. Binomial Theorem
2. Expand:
1. ${\left( {5x + 2} \right)^3}$
2. ${\left( {2x - 3y} \right)^4}$
3. In the expansion of ${\left( {\frac{1}{{7{x^2}}} - {x^3}} \right)^{10}}$ , determine:
1. the 4th term
2. the middle term
3. the constant term
4. In the expansion of ${\left( {3 - 2x} \right)^8}$ , determine the coefficient of the term containing ${X^5}$.
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###### Topic Notes
The Binomial Theorem is another method to help us expand binomials in a faster manner. It is particularly useful when we work on binomial expansions that involve binomials raised to high powers.