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Use Pascal’s triangle to expand the binomial.
(d–5y)6
To expand the binomial (d - 5y)^6 using Pascal's triangle, we will look at the 7th row of Pascal's triangle, as the term is raised to the power of 6.
The 7th row of Pascal's triangle is 1, 6, 15, 20, 15, 6, 1.
The terms of the expansion will be:
1*(d)^6*(-5y)^0 = d^6
6*(d)^5*(-5y)^1 = -30d^5y
15*(d)^4*(-5y)^2 = 150d^4y^2
20*(d)^3*(-5y)^3 = -750d^3y^3
15*(d)^2*(-5y)^4 = 1875d^2y^4
6*(d)^1*(-5y)^5 = -3125dy^5
1*(d)^0*(-5y)^6 = 3125y^6
Therefore, the expanded form of (d - 5y)^6 is:
d^6 - 30d^5y + 150d^4y^2 - 750d^3y^3 + 1875d^2y^4 - 3125dy^5 + 3125y^6.