Binomial Theorem using Pascal’s Triangle or nCr to find the coefficient then find the 27th term of (-3x+4y)55. Don’t forget to clean up the algebra.

That would be

55C26 (-3x)^29 (4y)^26

I'll let you do the arithmetic. Expect some large numbers!

.Which operations do you need to solve

11 x + 2 equals 89x+2=89​?

To find the 27th term of the binomial expansion of (-3x + 4y)^55, we can use the Binomial Theorem along with Pascal's Triangle or the nCr formula.

Binomial Theorem states that for any two real numbers a and b, and a positive integer n, the expansion of (a + b)^n can be written as:

(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nC(n-1) * a^1 * b^(n-1) + nCn * a^0 * b^n

Here, nCr represents the binomial coefficient and can be calculated using Pascal's Triangle or the formula:

nCr = n! / (r! * (n - r)!)

Note that n! represents the factorial of n, which is the product of all positive integers less than or equal to n.

To find the 27th term, we need to determine the proper values of a, b, n, and r in the expansion.

In this case, a = -3x, b = 4y, and n = 55. We want to find the 27th term, so r = 27 - 1 = 26 (since the terms start from 0).

Now, let's substitute these values into the Binomial Theorem:

(-3x + 4y)^55 = 55C0 * (-3x)^55 * (4y)^0 + 55C1 * (-3x)^54 * (4y)^1 + 55C2 * (-3x)^53 * (4y)^2 + ... + 55C25 * (-3x)^30 * (4y)^25 + 55C26 * (-3x)^29 * (4y)^26

To compute the coefficients, we can evaluate the binomial coefficients using Pascal's Triangle or the nCr formula.

Let's use the nCr formula:

nCr = 55! / (r! * (55 - r)!), where n = 55 and r = 26
55C26 = 55! / (26! * 29!)

Using this formula, the coefficients can be calculated.

Finally, simplify the algebraic expression by multiplying the coefficients with the appropriate powers of -3x and 4y, and then combine like terms to find the 27th term of the expansion.