Expand (3x - 2)⁴. Give the coefficient of x³, the coefficient of x, and the sum of all the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Expand . Give the coefficient of , the coefficient of , and the sum of all the coefficients.
Need a reminder? The key ideaShow
, with terms. The coefficients are row of Pascal's triangle, and each row adds up to . For the signs alternate.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The terms. .
Step 2. Simplify. .
Step 3. The sum. . This agrees with .
Answer: , and .
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