Expand Using Pascal's Triangle (2x-3y)^3

Problem

(2*x−3*y)3

Solution

1. Identify the row of Pascal's Triangle corresponding to the exponent n=3 The coefficients for the expansion are 1, 3, 3, 1$.

2. Set up the binomial expansion formula for (a+b)n where a=2*x and b=−3*y

3. Apply the coefficients and powers of a and b to each term of the expansion.

(2*x−3*y)3=1*(2*x)3*(−3*y)0+3*(2*x)2*(−3*y)1+3*(2*x)1*(−3*y)2+1*(2*x)0*(−3*y)3

4. Evaluate the powers for each term.

(2*x−3*y)3=1*(8*x3)*(1)+3*(4*x2)*(−3*y)+3*(2*x)*(9*y2)+1*(1)*(−27*y3)

5. Simplify the products to find the final terms.

(2*x−3*y)3=8*x3−36*x2*y+54*x*y2−27*y3

Final Answer

(2*x−3*y)3=8*x3−36*x2*y+54*x*y2−27*y3

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