Knowee
Questions
Features
Study Tools

To expand the expression (x + y)^8 using Pascal's triangle and the binomial theorem

Question

To expand the expression (x + y)^8 using Pascal's triangle and the binomial theorem

🧐 Not the exact question you are looking for?Go ask a question

Solution

To expand the expression (x + y)^8 using Pascal's triangle and the binomial theorem, follow these steps:

  1. Write down the 8th row of Pascal's triangle. Pascal's triangle is a triangular array of binomial coefficients. The 8th row (starting from 0) is: 1, 8, 28, 56, 70, 56, 28, 8, 1.

  2. Write down the binomial expression (x + y)^8.

  3. The binomial theorem states that (x + y)^n = Σ (n choose k) * x^(n-k) * y^k, where the sum is from k = 0 to n. In this case, n = 8.

  4. Expand the expression using the coefficients from Pascal's triangle and the powers of x and y from the binomial theorem:

    • For k = 0: 1 * x^8 * y^0 = x^8
    • For k = 1: 8 * x^7 * y^1 = 8x^7y
    • For k = 2: 28 * x^6 * y^2 = 28x^6y^2
    • For k = 3: 56 * x^5 * y^3 = 56x^5y^3
    • For k = 4: 70 * x^4 * y^4 = 70x^4y^4
    • For k = 5: 56 * x^3 * y^5 = 56x^3y^5
    • For k = 6: 28 * x^2 * y^6 = 28x^2y^6
    • For k = 7: 8 * x^1 * y^7 = 8xy^7
    • For k = 8: 1 * x^0 * y^8 = y^8
  5. Combine all the terms to get the expanded expression: (x + y)^8 = x^8 + 8x^7y + 28x^6y^2 + 56x^5y^3 + 70x^4y^4 + 56x^3y^5 + 28x^2y^6 + 8xy^7 + y^8.

This problem has been solved

Similar Questions

Determine the coefficient, a, for the term ax5y7 of the binomial expansion of (2x+y)12.

If the expansion of  (1 + x)m(1 − x)n , the coefficients of  x  and  x2  are 3 and -6 respectively, then:

Simply and express the following expression in terms of positive exponents:𝑥7⋅𝑦8𝑥5⋅𝑦5

Create an expression that shows "eight divided by two raised to the power of four".Then, evaluate the expression.Reset Submit

Expand using the bixombs axene. ( left(3+x-x^{2}right) ) ( left(3+x-x^{2}right)^{4} )

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.