Use pascal's triangle to expand the binomial

(d-5y)^6

show work.

In attached file you can see Pascal's triangle. Explanation for this triangle is following:

Then

Simplify it:

(d - 5y)⁶ = d⁶ - 30d⁵y + 375d⁴y² - 2500d³y³ + 9375d²y⁴ - 18750dy⁵ + 15625y⁶

The Problem:

Use Pascal's triangle to expand the binomial  (d - 5y)⁶.

The Process:

Look carefully at Pascal's triangle scheme in the attached picture.

Let us do a binomial expansion to:

, which comes from the following processing:

Alright, see carefully how the expansion of this binomial expression.

Thus, the expansion form of the binomial expression (d - 5y) ⁶ is

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Alternative Steps

We can also use Newton's Binomial Expansion.

Remember this

+ + +   +   + +

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Notes

Pascal's triangle in common is a triangular array of binomial coefficients. It is undoubtedly entitled after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Italy, Germany, Persia, India, and China.

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