Wikipedia
Binomial theorem - In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. Its simplest version states that for any real or complex numbers x and y, and any non-negative integer n. The binomial coefficient appearing in (1) may be defined in terms of the..
Binomial theorem - In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power ( x + y) n into a sum involving terms of the form ax b y c, where the coefficient of each term is a positive..
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Binomial Theorem
1. A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. 2. A statement involving natural number n is generally denoted by P(n). 3. A binomial is an algebraic expression o..
Applications of Binomial Theorem
Some Applications of Binomial Theorem for Fractional Index - If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (..
Some Applications of Binomial Theorem for Fractional Index - If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (..Binomial Theorem Summary
Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is a statement..
Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is a statement..Binomial Theorem Introduction
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical mann..
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical mann.. Binomial TheoremThisvideo briefly describes all the important concepts of Binomial Theorem, which is asked in various entrance examinations like IIT - JEE, AIEEE, DCE etc. This video has been created jointly by Sahil Study Circle and simplylearnt.com. You can enroll to Sahil Study Circle's online courses on simplylearnt by logging into simplylearnt at: www.simplylearnt.com
Binomial TheoremThisvideo briefly describes all the important concepts of Binomial Theorem, which is asked in various entrance examinations like IIT - JEE, AIEEE, DCE etc. This video has been created jointly by Sahil Study Circle and simplylearnt.com. You can enroll to Sahil Study Circle's online courses on simplylearnt by logging into simplylearnt at: www.simplylearnt.com
Question : Hello i need help expanding binomials using the binomial theorem.
1) (x+2)^8
2)(2x-3)^4
3)(x^2-y^2)^5
Answer : rather than trying to type the binomial theorem in ASCII, i'll just give the link to the wikipedia article: http://en.wikipedia.org/wiki/Binomial_theorem i'll work out 2) and you can try the others. (2x-3)^4=[(4!)/(0! 4!)](2x)^4+[(4!)/(1! 3!)](2x)^3(-3) +[(4!)/(2! 2!)](2x)^2(-3)^2+[(4!)/(3! 1!)](2x)(-3)^3 +[(4!)/(4! 0!)](-3)^4 =(2x)^4+4(2x)^3(-3)+6(2x)^2(9) +4(2x)(-27)+81 =16x^4-12(8x^3)+54(4x^2) -27(8x)+81 =16x^4-96x^3+216x^2-216x+81
Answer : rather than trying to type the binomial theorem in ASCII, i'll just give the link to the wikipedia article: http://en.wikipedia.org/wiki/Binomial_theorem i'll work out 2) and you can try the others. (2x-3)^4=[(4!)/(0! 4!)](2x)^4+[(4!)/(1! 3!)](2x)^3(-3) +[(4!)/(2! 2!)](2x)^2(-3)^2+[(4!)/(3! 1!)](2x)(-3)^3 +[(4!)/(4! 0!)](-3)^4 =(2x)^4+4(2x)^3(-3)+6(2x)^2(9) +4(2x)(-27)+81 =16x^4-12(8x^3)+54(4x^2) -27(8x)+81 =16x^4-96x^3+216x^2-216x+81
Question : I know how to expand it when it's given to me, but I'm not quite sure how to apply it (use it to solve word problems.) it would be really helpful if someone could give me an example problem and go through the steps of solving it.
if nothing else, what do the variables mean
or in other words:
if the theorem is (p + q)^n, what are p, q, and n?
Answer : The binomial theorem is used to expand expressions of the form (a+b)^n For example: (x + y)^3, (x + 8)^10, etc. a and b are just the two numbers or variables inside the brackets. The n is the exponent. If you wanted to expand (x + 8)^5, you would have to multiply out (X + 8) * (x+8) * ..... 5 times. This can be rather tedious. The binomial theorem is: (p + q)^n = Sum( fromk = 0 to k = n), of nCk * p^(n-k)q^k where nCk = n!/(n-k)!k!. If you want mor insight just google binomial theorem, and choose the site that you can understand best. Hope that helps. It's a bit cumbersome, nut less so that actually expanding something like (x + 8)^25
Answer : The binomial theorem is used to expand expressions of the form (a+b)^n For example: (x + y)^3, (x + 8)^10, etc. a and b are just the two numbers or variables inside the brackets. The n is the exponent. If you wanted to expand (x + 8)^5, you would have to multiply out (X + 8) * (x+8) * ..... 5 times. This can be rather tedious. The binomial theorem is: (p + q)^n = Sum( fromk = 0 to k = n), of nCk * p^(n-k)q^k where nCk = n!/(n-k)!k!. If you want mor insight just google binomial theorem, and choose the site that you can understand best. Hope that helps. It's a bit cumbersome, nut less so that actually expanding something like (x + 8)^25