What is the fourth term of (d – 4b)3?
(1 point)
Responses
b3
b 3
–b3
– b 3
64b3
64 b 3
–64b3
-64 b 3
To find the fourth term of (d – 4b)^3, we can use the binomial theorem.
The binomial theorem states that for any expression of the form (a + b)^n, the kth term is given by the formula:
T_k = nCk * a^(n-k) * b^k
In this case, our expression is (d - 4b)^3, so a = d, b = -4b, and n = 3.
Plugging these values into the formula, we can determine the fourth term (k = 4):
T_4 = 3C4 * d^(3-4) * (-4b)^4
Since 3C4 = 0 (as 3 choose 4 is not defined), the fourth term is equal to zero.
Therefore, the fourth term of (d - 4b)^3 is 0.
To find the fourth term of (d – 4b)3, we can use the binomial theorem or expand the expression using the rules of exponents.
The binomial theorem states that for any (a + b)n, the kth term is given by the formula:
(nCk) * a^(n-k) * b^k
In our case, (d – 4b)3 is equivalent to (d – 4b) * (d – 4b) * (d – 4b).
Expanding the expression, we get:
(d – 4b)(d – 4b)(d – 4b) = (d^2 – 8bd + 16b^2)(d – 4b) = d^3 – 8bd^2 + 16b^2d – 4bd^2 + 32b^2d – 64b^3
Now, let's identify the fourth term. The terms are arranged in descending powers of d, so the fourth term will have d^1 (or simply d, since the exponent is 1). The fourth term will have a coefficient that combines the coefficients of the individual terms d^1, b^0, and b^3.
Looking at the expanded expression, the fourth term is -8bd^2.
Therefore, the fourth term of (d – 4b)3 is -8bd^2.