Question

Use pascal's triangle to expand (x-y)7​

Answer 1

To expand (x-y)^7 using Pascal's triangle, we use the coefficients from the 7th row of the triangle. The expanded form is x^7 - 7x^6y + 21x^5y^2 - 35x^4y^3 + 35x^3y^4 - 21x^2y^5 + 7xy^6 - y^7.

Step-by-step explanation:

To expand (x-y)^7 using Pascal's triangle, we will use the coefficients from the 7th row of the triangle. Pascal's triangle is a triangle of numbers where each number is the sum of the two numbers above it. The 7th row of Pascal's triangle is 1, 7, 21, 35, 35, 21, 7, 1. We will use these coefficients to expand (x-y)^7 as:

1. Start with the first term, x^7.
2. Multiply the first coefficient, 1, by x^7.
3. Continue in the same manner for the remaining terms, using alternating signs and increasing powers of x and decreasing powers of y.
4. The expanded form of (x-y)^7 is x^7 - 7x^6y + 21x^5y^2 - 35x^4y^3 + 35x^3y^4 - 21x^2y^5 + 7xy^6 - y^7.