Use Pascal’s triangle to expand the binomial. (d-5y)^6
To expand the binomial (d-5y)^6 using Pascal's triangle, we need to find the coefficients for each term.
Pascal's triangle looks like this:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
The 6th row of Pascal's triangle is: 1 5 10 10 5 1
Therefore, the expansion of (d-5y)^6 is:
1(d^6) + 5(d^5)(-5y) + 10(d^4)(-5y)^2 + 10(d^3)(-5y)^3 + 5(d^2)(-5y)^4 + 1(d)(-5y)^5
= d^6 - 30d^5y + 300d^4y^2 - 1500d^3y^3 + 3750d^2y^4 - 3125dy^5