If (x^2-5y)^3 is written in expanded form, what is the coefficient of x^2y^2 term?

Question

Please help with this question ASAP

Answer 1

I just answerd that for you. I said: A binomial is a polynomial with two terms. We're going to look at the Binomial Expansion Theorem, a shortcut method of raising a binomial to a power.

(x+y)⁰ = 1 
(x+y)¹ = x + y 
(x+y)² = x² + 2xy + y² 
(x+y)³ = x³ + 3x²y + 3xy² + y³ 
(x+y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴ 
(x+y)⁵ = x⁵ + 5x⁴y + 10x³y² +10x²y³ + 5xy⁴ + y⁵

There are several things that you hopefully have noticed after looking at the expansion

• There are n+1 terms in the expansion of (x+y)ⁿ
• The degree of each term is n
• The powers on x begin with n and decrease to 0
• The powers on y begin with 0 and increase to n
• The coefficients are symmetric

Pascal's Triangle

Pascal's Triangle, named after the French mathematician Blaise Pascal is an easy way to find the coefficients of the expansion.

Each row in the triangle begins and ends with 1. Each element in the triangle is the sum of the two elements immediately above it.

              1
            1   1
          1   2   1
        1   3   3   1
      1   4   6   4   1
    1   5  10  10   5   1
  1   6  15  20  15   6   1
1   7  21  35  35  21   7   1

 

Answer 2

(x+y)⁰ = 1 
(x+y)¹ = x + y 
(x+y)² = x² + 2xy + y² 
(x+y)³ = x³ + 3x²y + 3xy² + y³ 
(x+y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴ 
(x+y)⁵ = x⁵ + 5x⁴y + 10x³y² +10x²y³ + 5xy⁴ + y⁵

There are several things that you hopefully have noticed after looking at the expansion

• There are n+1 terms in the expansion of (x+y)ⁿ
• The degree of each term is n
• The powers on x begin with n and decrease to 0
• The powers on y begin with 0 and increase to n
• The coefficients are symmetric

Pascal's Triangle

Pascal's Triangle, named after the French mathematician Blaise Pascal is an easy way to find the coefficients of the expansion.

Each row in the triangle begins and ends with 1. Each element in the triangle is the sum of the two elements immediately above it.

              1
            1   1
          1   2   1
        1   3   3   1
      1   4   6   4   1
    1   5  10  10   5   1
  1   6  15  20  15   6   1
1   7  21  35  35  21   7   1