Powers of the Binomial
Key Questions
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Answer:
The power of a binomial is the value of
n in the binomial expression(a+x)^n .Explanation:
For any value of
n , then^"th" power of a binomial is given by:(x+y)^n=x^n +nx^(n-1)y +(n(n-1))/2x^(n-2)y^2 + … + y^n The general formula for the expansion is:
(x+y)^n = sum_(k=0)^n (n!)/((n-k)!k!)x^(n-k)y^k The coefficients for varying
x andy can be arranged to form Pascal's triangle.
The
n^"th" row in the triangle gives the coefficients of the terms in the(n-1)^"th" power of the polynomial.
Ernest Z.
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1
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Aug 29 2015
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Answer:
(a+b)^3 = a^3+3a^2b+3ab^2+b^3 Explanation:
The coefficients
1, 3, 3, 1 can be found as a row of Pascal's triangle:For other powers of a binomial use a different row of Pascal's triangle.
For example:
(a+b)^5 = a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5 How about
(2x-5)^3 or similar?Let
a=2x andb=-5 to find:(2x-5)^3 = (a+b)^3 = a^3+3a^2b+3ab^2+b^3 =(2x)^3+3(2x)^2(-5)+3(2x)(-5)^2+(-5)^3 =8x^3-60x^2+150x-125 
George C.
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2
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Oct 26 2015
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Answer:
I am not sure about what you need, but have a look:
Explanation:
If you have a binomial such as
(a+b) and you square it you get:
(a+b)^2
but this is the same as:
(a+b)(a+b) exactly as
4^2=4xx4 .The result of
(a+b)(a+b) is interesting because you need to multiply each term of the first bracket by each term of the second and add the results!
(a+b)(a+b)=a*a+a*b+b*a+b*b=a^2+2ab+b^2 Try by yourself with a difficult one:
(a-b)^2 remembering to consider the signs of each term!
Gió
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1
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Aug 16 2015