Can you check my answers?
1.Find the 5th term in the expansion of the binomial.
(2x - 4)8
-458,752x3
286,720x4
458,752x3
35,840x4
answer: d
2.Find the 3rd term in the expansion of the binomial.
(x - 2y)12
264x10y2
1760x9y3
-264x10y2
-1760x9y3
answer:a
#1
term(5) = C(8,4) (2x)^4 (-4)^4
= 70(16x^4)(256)
= 286720 x^4 <-------- B
general term of (a+b)^n:
term (k+1) = C(n,k) * (a)^(k-1) * b^k
#2, correct
Sure, I can help you check your answers.
To find a specific term in the expansion of a binomial, we use the binomial theorem formula:
T(n+1) = (n C r) * (a^(n-r)) * (b^r)
Where:
T(n+1) = the (n+1)th term in the expansion
n = the power or degree of the binomial (in our case, 8 and 12)
r = the term we want to find (in our case, 5 and 3)
a = the first term of the binomial (in our case, 2x and x)
b = the second term of the binomial (in our case, -4 and -2y)
(n C r) = the combination coefficient, which represents the number of ways to choose r objects out of n.
Now, let's apply the formula to check your answers:
1. Find the 5th term in the expansion of (2x - 4)^8:
T(5) = (8 C 4) * (2x)^(8-4) * (-4)^4
T(5) = 70 * (2x)^4 * 256
T(5) = 70 * 16x^4 * 256
T(5) = 286,720x^4
Your answer is correct: 286,720x^4.
2. Find the 3rd term in the expansion of (x - 2y)^12:
T(3) = (12 C 2) * (x)^(12-2) * (-2y)^2
T(3) = 66 * x^10 * 4y^2
T(3) = 264x^10y^2
Your answer is correct: 264x^10y^2.
Great job! Both of your answers are correct. If you have any more questions or need further assistance, feel free to ask.