How do you find the 5th term in the expansion of the binomial #(5a+6b)^5#?

Answer 1

Cora Alexander

#32400ab^4#

The expansion will have six terms starting with #a^5# and ending with #b^5# Fifth term will be #5C(5-1)*a^(5-4)*b^4#

Let a be (5a) and b be (6b).

We also know #5C4 = 5C1 = 5#.

By replacing in the fifth term, we obtain

#= 5*(5a)*(6b)^4 = 32400*a*b^4#

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Answer 2

Christian Antunez

#32400ab^4#

The fifth word that descends is a:

#5^1(5C4)a^1 6^4b^4= 5*5*1296a^1b^5=32400ab^4#

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Answer 3

Serenity Jones

To find the 5th term in the expansion of the binomial (5a + 6b)^5, we use the binomial theorem. The general term in the expansion of (a + b)^n is given by the formula: T_r = C(n, r) * a^(n-r) * b^r, where n is the exponent, r is the term number (starting from 0), and C(n, r) is the binomial coefficient, also known as "n choose r."

For the 5th term (r = 4), we substitute n = 5 and r = 4 into the formula: T_4 = C(5, 4) * (5a)^(5-4) * (6b)^4

First, we calculate the binomial coefficient: C(5, 4) = 5! / (4! * (5 - 4)!) = 5

Then, we simplify the terms: T_4 = 5 * (5a)^1 * (6b)^4 = 5 * 5a * (1296b^4) = 25a * 1296b^4 = 32400ab^4

Therefore, the 5th term in the expansion of (5a + 6b)^5 is 32400ab^4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.