Algebraic expansions to memorize
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Algebraic expansions to memorize
Key algebraic expansions include:
(a^2b^2)= (a+b)(ab)
(a+b)^2= a^2 +2ab+ b^2
(ab)^2= a^2 2ab+ b^2
(a+b)^3= (a+b)(a^2 ab +b^2)
(ab)^3= (ab)(a^2 +ab +b^2)
The above algebraic expansions will be helpful for both MathCounts, factoring equations, and math class. Comment below if you have anything to add.
(a^2b^2)= (a+b)(ab)
(a+b)^2= a^2 +2ab+ b^2
(ab)^2= a^2 2ab+ b^2
(a+b)^3= (a+b)(a^2 ab +b^2)
(ab)^3= (ab)(a^2 +ab +b^2)
The above algebraic expansions will be helpful for both MathCounts, factoring equations, and math class. Comment below if you have anything to add.
Archis Admin
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Re: Algebraic expansions to memorize
If you take A+B^3 and you want to find out the answer, then imagine pascal's triangle. If you want to find out what a+b^5 is then find the fifth line in pascal's triangle which is 1 5 10 10 5 1. These are the coefficients. As for the variables, the first would be a^5 then a^4b then a^4b^3 and so on until the last one which should be b^5. This will help so much with FOILrelated problems.
theonlyMattinMathCounts Novice Poster
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Re: Algebraic expansions to memorize
theonlyMattinMathCounts wrote:If you take A+B^3 and you want to find out the answer, then imagine pascal's triangle. If you want to find out what a+b^5 is then find the fifth line in pascal's triangle which is 1 5 10 10 5 1. These are the coefficients. As for the variables, the first would be a^5 then a^4b then a^4b^3 and so on until the last one which should be b^5. This will help so much with FOILrelated problems.
Yup. For those people who enjoy collecting theorems, this is known as the Binomial Theorem.
This can prove very efficient for long arithmetic problems as in:
Determine (5^3) + 3(5^2)(2) + 3(5)(4) + 2^3
 Spoiler:
 5 second problem. Note that it is (a+b)^3, where a and b are 5 and 2. (5+2)^3= 343.
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