expand the binomial- (5y-11)^4

To expand the binomial (5y-11)^4, we can use the binomial theorem formula, which states that for any real numbers a and b and 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

where C(n, k) represents the binomial coefficient, which is given by n!/[(n-k)!k!]. Let's apply this formula to (5y-11)^4:

(5y-11)^4 = C(4, 0)(5y)^4 (-11)^0 + C(4, 1)(5y)^3 (-11)^1 + C(4, 2)(5y)^2 (-11)^2 + C(4, 3)(5y)^1 (-11)^3 + C(4, 4)(5y)^0 (-11)^4

Simplifying each term:

= 1(5y)^4 (1) + 4(5y)^3 (-11) + 6(5y)^2 (121) + 4(5y)(-1331) + 1(1)(14641)

= 625y^4 + 4(-165y^3) + 6(605y^2) + 4(-6655y) + 14641

= 625y^4 - 660y^3 + 3630y^2 - 26620y + 14641

Therefore, the expanded form of (5y-11)^4 is 625y^4 - 660y^3 + 3630y^2 - 26620y + 14641.