4 Strategies To Solve A Binomial Proof
Posted on September 8, 2017 by Matrix Education
Often binomial proofs can be the most difficult questions in the Maths Extension 1 exam, with students struggling to approach these complex proofs. However, there are certain strategies that you can use to tackle these questions. Your first step is to expand , or a similar expression if otherwise stated in the question.
Your next step is to consider the four strategies below.
When to use it: Examine the final term in your expansion and see if replacing with a number will make your expansion look like the answer. However, if you are unsure then it is fine to use trial and error. This won’t take too long as the only substitutions I’ve only ever seen required are x= -1, -1, 0, 1 or 2. Consider the example below.
When to use it: Look for signs of differentiation in the answer, most notably anything to the power of (n-1), such as n2n-1. This indicates that you must differentiate both sides of your expanded equation. Very often after differentiating, you need to make a substitution for x. Note that some questions may require you to differentiate twice.
When to use it: Look for signs of integration. Something raised to the power of (n + 1) in the answer is a clear sign. When integrating, consider using a definite integral; the limits are often easy numbers such as x = 0, ±1, or ±2. Note that you may be required to integrate twice. In this situation, integrate without limits, which will result in a +C . You can easily find out this constant by substituting x= 0 into both sides of the equation. Once C is found, you can then integrate again if required.
4. Expanding the binomial in 2 different ways
With this in mind we can recognize that we must expand the binomial in the question in 2 ways when the power of the expansions differ. For example, if the question is to prove , then you must consider the expansion and then equate coefficients of like terms.
Click here to download the solutions to these examples.
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