(d–5y)^6

Answer 1

To expand the expression (d - 5y)^6, you can use the binomial theorem.

The binomial theorem states that for any positive integer n:

(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n

In this case, a = d and b = -5y.

Using the binomial theorem, the expansion of (d - 5y)^6 can be written as:

C(6, 0) * d^6 * (-5y)^0 + C(6, 1) * d^5 * (-5y)^1 + C(6, 2) * d^4 * (-5y)^2 + C(6, 3) * d^3 * (-5y)^3 + C(6, 4) * d^2 * (-5y)^4 + C(6, 5) * d^1 * (-5y)^5 + C(6, 6) * d^0 * (-5y)^6

Simplifying each term gives:

1 * d^6 * 1 + 6 * d^5 * (-5y) + 15 * d^4 * (25y^2) + 20 * d^3 * (-125y^3) + 15 * d^2 * (625y^4) + 6 * d^1 * (-3125y^5) + 1 * d^0 * (15625y^6)

Therefore, the expanded expression of (d - 5y)^6 is:

d^6 - 30d^5y + 375d^4y^2 - 2500d^3y^3 + 9375d^2y^4 - 18750dy^5 + 15625y^6