use pascals triangle to expand the binomial

Question

(d-5y)^6

Answer 1

To expand (d - 5y)^6 using Pascal's Triangle, we will use the following pattern:

1. Start with the sixth row of Pascal's Triangle (1 6 15 20 15 6 1).
2. Write the coefficients in front of the terms in decreasing order, starting with the first term being raised to the power of 6 and the second term being raised to the power of 0.

Using Pascal's Triangle, we have:

(d - 5y)^6 = 1*d^6 + 6*d^5*(-5y) + 15*d^4*(-5y)^2 + 20*d^3*(-5y)^3 + 15*d^2*(-5y)^4 + 6*d*(-5y)^5 + 1*(-5y)^6

Simplifying each term:

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

Therefore, (d - 5y)^6 = d^6 - 30d^5y + 375d^4y^2 - 2500d^3y^3 + 9375d^2y^4 - 18750dy^5 + 15625y^6.