What is the standard form of #y= (2x+3x^2)(x+3) -(x-2)^3#?
1 Answer
Explanation:
To answer this question, you will have to simplify the function. Begin by using the FOIL Method to multiply the first term:
Simplifying this yields:
We now have the first term simplified. To simplify the second term, we can use the
Binomial Theorem, a useful tool when working with polynomials. One of the main points of the theorem is that the coefficients of an expanded binomial can be determined using a function called the choose function. The specifics of the choose function are more of a probability concept, so there's no need to go into it right now.
However, a simpler way to use the Binomial Theorem is
Pascal's Triangle. The numbers in Pascal's Triangle for a certain row number will correspond to the coefficients of the expanded binomial for that row number. In the case of cubing, the third row is
Notice how we decrease the power of
Simplifying gives us:
To simplify, we can subtract the second term from the first:
Standard form means that the terms of the polynomial are ordered from highest degree to lowest. Because this has already been done, your final answer is:
