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I think an example will help most people see it better than just an explanation/answer. So first a few examples are presented and than a general answer.

Start with (1+x)2 = 1+2x+x2 and look at the coefficients of the results you will see that they are 1, 2, 1. Now do it for (1+x)3 and they are 1, 3, 3, 1. These, of course, are the lines from Pascal's Triangle. I put the first part of the triangle below (in left-justified form). You should notice that when the exponent is 2, we use the third line and when the exponent is 3, we use the fourth line of the triangle.

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

In case you wonder about the first two rows. Look at (1+x)0 and

(1+x)1, their coefficients come from those two rows.

Now look at (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 which is more general and of course the coefficients come from the 5th line of the triangle.

So the answer to the question is that if we look at the binomial (a + b)n

The n+1 row of Pascal's triangle gives us the coefficients of the expanded form of the binomial. Seeing the examples first often makes this easier to see and understand. It is the n+1 row because the first row of the triangle is any binomial with an exponent of 0.

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Q: How is Pascal's triangle related to the Binomial Theorem?
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How is the pascal triangle and the binomial expansion related?

If the top row of Pascal's triangle is "1 1", then the nth row of Pascals triangle consists of the coefficients of x in the expansion of (1 + x)n.


How do you find a side of a triangle?

If it's a right triangle, use pythagorean's theorem (a2+b2=c2) to solve it. = If it's an oblique triangle, use the law of sines or cosines (see related link)


What is binomial expansion theorem?

We often come across the algebraic identity (a + b)2 = a2 + 2ab + b2. In expansions of smaller powers of a binomial expressions, it may be easy to actually calculate by working out the actual product. But with higher powers the work becomes very cumbersome.The binomial expansion theorem is a ready made formula to find the expansion of higher powers of a binomial expression.Let ( a + b) be a general binomial expression. The binomial expansion theorem states that if the expression is raised to the power of a positive integer n, then,(a + b)n = nC0an + nC1an-1 b+ nC2an-2 b2+ + nC3an-3 b3+ ………+ nCn-1abn-1+ + nCnbnThe coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficientnCr = n!r!(n-r)!It may be interesting to note that there is a pattern in the binomial expansion, related to the binomial coefficients. The binomial coefficients at the same position from either end are equal. That is,nC0 = nCn nC1 = nCn-1 nC2 = nCn-2 and so on.The advantage of the binomial expansion theorem is any term in between can be figured out without even actually expanding.Since in the binomial expansion the exponent of b is 0 in the first term, the general term, term is defined as the (r+1)th b term and is given by Tr+1 = nCran-rbrThe middle term of a binomial expansion is [(n/2) + 1]th term if n is even. If n is odd, then terewill be two middle terms which are [(n+1)/2]th and [(n+3)/2]th terms.


How are the sides realated in a right triangle?

One way that they are related is called the Pythagorean theorem. C squared = b squared + c squared. c being the hypotenuse, and a and b being the legs. If it is a special right triangle, such as a 45-45-90 or 30-60-90, there are other ratios which describe their relationships.


How are the terms of binomial being squared related to the middle terms of the product?

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Related questions

How is the pascal triangle and the binomial expansion related?

If the top row of Pascal's triangle is "1 1", then the nth row of Pascals triangle consists of the coefficients of x in the expansion of (1 + x)n.


How are the side lengths of a 30º60º90º triangle related?

It is a right angle triangle and the sum of its squared sides is equal to its squared hypotenuse in accordance with Pythagoras' theorem


How do you find a side of a triangle?

If it's a right triangle, use pythagorean's theorem (a2+b2=c2) to solve it. = If it's an oblique triangle, use the law of sines or cosines (see related link)


How are the Pythagorean Theorem and distance formula related to each other?

Because a right angle triangle can be formed by the given coordinates and the length of the line is the hypotenuse of the triangle and so by using Pythagoras' theorem its length or distance can be found. Distance formula: square root of [(x1-x2)^2 plus (y1-y2)^2)]


What is binomial expansion theorem?

We often come across the algebraic identity (a + b)2 = a2 + 2ab + b2. In expansions of smaller powers of a binomial expressions, it may be easy to actually calculate by working out the actual product. But with higher powers the work becomes very cumbersome.The binomial expansion theorem is a ready made formula to find the expansion of higher powers of a binomial expression.Let ( a + b) be a general binomial expression. The binomial expansion theorem states that if the expression is raised to the power of a positive integer n, then,(a + b)n = nC0an + nC1an-1 b+ nC2an-2 b2+ + nC3an-3 b3+ ………+ nCn-1abn-1+ + nCnbnThe coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficientnCr = n!r!(n-r)!It may be interesting to note that there is a pattern in the binomial expansion, related to the binomial coefficients. The binomial coefficients at the same position from either end are equal. That is,nC0 = nCn nC1 = nCn-1 nC2 = nCn-2 and so on.The advantage of the binomial expansion theorem is any term in between can be figured out without even actually expanding.Since in the binomial expansion the exponent of b is 0 in the first term, the general term, term is defined as the (r+1)th b term and is given by Tr+1 = nCran-rbrThe middle term of a binomial expansion is [(n/2) + 1]th term if n is even. If n is odd, then terewill be two middle terms which are [(n+1)/2]th and [(n+3)/2]th terms.


How are the following terms related Binomial Nomenclature Genus Species?

in relationto binomial nomenclature, what is our genus and species?``


What is the binomial system used by scientists?

The related link should help you.


How is an isosceles triangle related to an isosceles trapezoid?

how is an isoscelels trapezoid related to a isosceles triangle


What type of circuit is Superposition theorem related to?

As we know that: The superposition theorem is that the linear responses in a circuit can be derived by summing the responses of the independent sources algebraically, therefore, it related to LINEAR CIRCUITS!


When and how to use the Pythagorean theorem?

Definition:Pythagorean theorem (also known as Pythagoras' theorem) is a mathematical statement about the relation among the three sides of a right triangle (right-angled triangle).It states:"In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides."In any right-angled triangle, if the sides forming the right-angle are known as a and b and the hypotenuse as c, then the relation among the three sides of a right triangle is given by this equation: a2 + b2 = c2.When to use it:If the length of two sides of a right angled triangle are already known, you can find the unknown length of the third side.How to use it:As you know the relation among the three sides of a right triangle is represented by the equation a2 + b2 = c2 , substitute the known values in the equation and find out the length of the third side by solving the equation.See the related link.


How much surface pressure does Jupiter have?

The surface pressure on Jupiter varies between 20 and 200 kilo pascals. On Earth, the surface pressure is around 100 kilo pascals. See related link for more information


How are the sides realated in a right triangle?

One way that they are related is called the Pythagorean theorem. C squared = b squared + c squared. c being the hypotenuse, and a and b being the legs. If it is a special right triangle, such as a 45-45-90 or 30-60-90, there are other ratios which describe their relationships.