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:

coefficient in 0th row is coefficients in 1st row are coefficients of coefficients in 2nd row are coefficients of coefficients in 3rd row are coefficients of and so oncoefficients in 6th row are coefficients of

Then

Simplify it:

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

Further explanation

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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Another example

2nd term in expansion of is -6x.The coefficient of x⁻¹ in expansion of is ³/₂.Learn moreWhich expression is equivalent to the product of a binomial and a trinomial after it has been fully simplified? A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 Which binomial is not a divisor of x³ - 11x² + 16x + 84?

Delta airlines or untied

X=14 hope it !