Question 409349: What is the answer of the following espression: (x-2)^3 ? and can you pls. write the solutions. Thank you and GOD bless! Found 2 solutions by jsmallt9, richard1234:Answer by jsmallt9(3758) (Show Source):
Unless you have learned the Binomial Theorem and know how to use it, there is no pattern/formula that will help us cube x-2. But most people are supposed to learn patterns/formulas for squaring a binomial: and . We will take advantage of one of these.
First we can rewrite your expression as:
By doing this we can take advantage of the squaring pattern. We will use the second one because it has a minus between the two terms just like (x-2):
which simplifies to:
For the last part will will have to multiply this out by hand. This means we will multiply each term of the first factor times each term of the second factor. (Since there are 3 terms in the first factor and 2 terms in the second factor, there will be a total of 6 multiplications!) After multiplying we combine like terms, if any.
Before we start multiplying I prefer to rewrite all subtractions as additions of the opposite. There are many reasons this is a good idea.
Multiplying each term of one factor by each term of the other factor:
which simplifies to:
Adding the like terms we get:
or
(