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Q: How is the pascal triangle and the binomial expansion related?

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yang hui discovered pascal's triangle it was discovered 300 years later by pascal

The coefficients of the binomial expansion of (1 + x)n for a positive integer n is the nth row of Pascal's triangle.

For binomial expansions. (When you have to multiply out many brackets, binomial expansion speeds things up greatly).

Pascal's triangle shows the constant for each term if the equation is (x+y) to a number, which is the line number in Pascal's triangle, for a binomial expansion you can use Pascal's triangle but you have to multiply that by the constants on x and y raised to x's and y's exponent multiplied by the number the binomial is being raised to. (ax^b + cy^d) ^e = the number in Pascal's triangle for e times (a^ (b times e)) times (c ^(d times e)) which gives the constant for that term

It generates binomial coefficients.

The expanded binomial is another name for Pascal's triangle.

Blaise Pascal (France, 1623-1662) His inventions include the hydraulic press and the syringe.Hope this helps!Pascal was a mathematician in the 17th century. He described Pascal's Triangle, possibly one of the easiest methods of binomial expansion.

Pascal continued to influence mathematics throughout his life. His Traité du triangle arithmétique ("Treatise on the Arithmetical Triangle") of 1653 described a convenient tabular presentation for binomial coefficients, now called Pascal's triangle.

The binomial expansion is the expanded form of the algebraic expression of the form (a + b)^n.There are slightly different versions of Pascal's triangle, but assuming the first row is "1 1", then for positive integer values of n, the expansion of (a+b)^n uses the nth row of Pascals triangle. If the terms in the nth row are p1, p2, p3, ... p(n+1) then the binomial expansion isp1*a^n + p2*a^(n-1)*b + p3*a^(n-2)*b^2 + ... + pr*a^(n+1-r)*b^(r-1) + ... + pn*a*b^(n-1) + p(n+1)*b^n

The Pascal's triangle is used partly to determine the coefficients of a binomial expression. It is also used to find the number of combinations taken n at a time of m things .

Yes and no. See related link. The triangle methodology was employed in 1653 by Pascal, but not published until 1665. Pascal died in 1662.

Pascal's Triangle is an illustration of the coefficients of a binomial expansion. (There are also other patterns within the triangle, but it is primarily taught in relation to binomial expansion.) Each row begins and ends with the number one. The elements in each row are the sum of the two numbers above it in the previous row and continues indefinitely: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

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