Question

Expand (x-y)3 using Pascal triangle

Answer 1

To expand (x-y)³ using Pascal’s triangle, we can write:

1

1 1

1 2 1

1 3 3 1

Each row of the triangle represents the coefficients of the binomial expansion of (a+b)ⁿ, with the top row being n=0.

So for (x-y)³, we take the fourth row of the triangle (starting with n=0), and substitute x and y into the formula, alternating the signs of y:

1x³ + 3x²(-y) + 3x(-y)² + 1(-y)³

= x³ - 3x²y + 3xy² - y³

Thus, (x-y)³ = x³ - 3x²y + 3xy² - y³.