How many terms are in a binomial?
two terms
binomial: A polynomial consisting of two terms, or monomials, separated by an addition or subtraction symbol.
Is a binomial coefficient a combination?
A binomial coefficient equals the number of combinations of r items that can be selected from a set of n items. It also represents an entry in Pascal’s triangle. These numbers are called binomial coefficients because they are coefficients in the binomial theorem.
How do you find the sum of a binomial expansion?
According to the theorem, it is possible to expand the power (x+y)n ( x + y ) n into a sum involving terms of the form axbyc a x b y c , where the exponents b and c are nonnegative integers with b+c=n b + c = n , and the coefficient a of each term is a specific positive integer depending on n and b .
What is the constant term of a binomial expansion?
We can see that the general term becomes constant when the exponent of variable x is 0 . Therefore, the condition for the constant term is: n−2k=0⇒ k=n2 . In other words, in this case, the constant term is the middle one ( k=n2 ).
Is the sum of two binomials always a binomial?
The square of a binomial is always the sum of: The first term squared, 2 times the product of the first and second terms, and the second term squared.
What is a binomial sum?
A binomial is a sum of two terms. a + b. A trinomial is a sum of three terms, while a multinomial is more than three. Quadratic is another name for a polynomial of the 2nd degree.
What is the formula for binomial theorem?
For a binomial involving subtraction, the theorem can be applied by using the form (x − y) n = (x + (−y)) n. This has the effect of changing the sign of every other term in the expansion:
What is the sum of X and Y?
You are also told the the sum of x and y is S so x + y = S. Solving this equation for y gives y = S – x. Substitute this value for y into the product expression to get P = xy = x (S – x)