Binomial Expansion - Revision

Binomial Expansion is use to expand an algebraic expression. It is less messy as compare to using the "rainbow method

Review the examples on the right to refresh your memory.

​Example 1:

​Example 2:

Multiple Choice

Q1 Find the first 4 terms of the expansion $$\left(4-\frac{x}{2}\right)^5$$

• 1 $$1024-640x+160x^2-20x^3+...$$

• 2 $$1024-640x+160x^2-45x^3+...$$

• 3 $$1024-640x+160x^2+80x^3+...$$

​Can you remember how to find an unknown term without expanding the entire expression?

Match

Q2 Find the general term of each expansion. Match to the correct answer.

• $$C_r^8\left(5x\right)^{\left(8-r\right)}\left(-3\right)^r$$

• $$C_r^8\left(3x\right)^{\left(8-r\right)}\left(-5\right)^r$$

• $$C_r^5\left(8x\right)^{\left(5-r\right)}\left(-3\right)^r$$

• $$C_r^3\left(5x\right)^{\left(3-r\right)}\left(-8\right)^r$$

• $$\left(5x-3\right)^8$$

• $$\left(3x-5\right)^8$$

• $$\left(8x-3\right)^5$$

• $$\left(5x-8\right)^3$$

​The video on the left is another example on how to find the coefficient of a particular term. In this case, it is x²

Fill in the Blanks

Q3 In the expansion $\left(2x-\frac{1}{x^2}\right)^{12}$ , find the term independent of x, i.e. x⁰

Fill in the Blanks

Q4 In the SAME expansion $\left(2x-\frac{1}{x^2}\right)^{12}$ , find the term in $\frac{1}{x^{15}}$