- #1
look416
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Homework Statement
Determine the coefficient of p4q7 in the expansion of (2p-q)(p+q)10
Homework Equations
The Attempt at a Solution
sry, i can't attempt to solve this coz i don't even know how to expand this using formula
look416 said:well i know
but does this related to (a+b)n
look416 said:extremely required help
lanedance said:might help, to see what rockfreak is implying, if you write it as
(2p)(p+q)10 - q(p+q)10
now think about which terms you need to look at for p4q7
rock.freak667 said:because you can expand out (p+q)10 and you can multiply out the terms which will give you p4q7
look416 said:well that one is definitely wrong
because (2p-q)(p+q) is not equal to (2p)(p+q) - q(p+q)
look416 said:well no other methods?
because this method will definitely cause a lot of hardwork
lanedance said:have a look at this to find out about the binomial expansion
http://en.wikipedia.org/wiki/Binomial_theorem
lanedance said:if you use the binomial expansion theorem, this will tell you what the terms are without doing all the multiplication. do you know what the binomial expansion theorem is?
you just have to decide which terms you want to find - see previous post
lanedance said:really? try multiplying both sides out
Binomial expansion is a mathematical process used to expand an expression with two terms raised to a power. It involves using the binomial coefficients, which are the numbers that appear in front of each term, to determine the terms in the expansion.
The coefficient of p4q7 in (2p-q)(p+q)10 is the number that appears in front of the term p4q7 in the expanded form of the expression. In this case, it is the number that represents how many times p4q7 appears in the expansion.
To find the coefficient of a specific term in a binomial expansion, you can use the binomial theorem or Pascal's triangle. The binomial theorem is a formula that can be used to find the coefficient of a specific term, while Pascal's triangle is a visual tool that can help you identify patterns and determine the coefficient.
The coefficient in a binomial expansion is important because it gives information about the number of times a certain term appears in the expanded form of the expression. It also helps in simplifying and solving equations involving binomial expressions.
Binomial expansion has various applications in real-life situations, such as in probability and statistics, finance, and physics. For example, it can be used to calculate the probability of certain outcomes in a given experiment or to determine the growth of investments over time. In physics, it is used to model and analyze physical phenomena involving two terms raised to a power.