What is the coefficient of x4y4 in the expansion of (x + y)8?
2 answers:
Answer:
70
Step-by-step explanation:
If you use Pascal's Triangle, you will need 9 lines, since there are 9 terms in a binomial raised to the 8th power. Those 9 terms are:
1, 8, 28, 56, 70, 56, 28, 8, 1
The first expansion through the one we need are below (I hope you know how to use Pascal's Triangle!):
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8x - 2(x + 1) = 2(3x - 1)
First, expand to remove parenthesis. / Your problem should look like:
Second, subtract 8x - 2x - 2 to get 6x - 2. / Your problem should look like:
Third, both sides are equal, so there are infinite solutions. The equation is always true.
Answer: infinite solutions
First, expand to remove parenthesis. / Your problem should look like:
Second, subtract 8x - 2x - 2 to get 6x - 2. / Your problem should look like:
Third, both sides are equal, so there are infinite solutions. The equation is always true.
Answer: infinite solutions
Multiplication and division with the powers of ten
So, when multiply powers of ten, all you have to do add up the powers.
The reverse goes when you are dividing. You would subtract the powers.
9 x 10^7 => 3 x 10^3
The words " how many times as large as " indicates that we are going to divide the two, making it look like this:
Divide the 9 by 3 you get 3
Then subtract 10^3 from 10^7
Therefore, the answer is 3 x 10^4, or A