Question

1. (2y -x)2 =2. (2xy + 3y)2 =3. (3x - 1)3 =4. a2 - 81 B\25. (4x -y) (4x +y) =

Answer 1

1. (2y -x)2 = 4y−2x
2. (2xy + 3y)2 =4xy+6y
3. (3x - 1)3 =9x−3
5. (4x -y) (4x +y)=  16x^2+4xy−4yx−y^2=16x^2−y^2

Answer 2

Let's solve each of the given expressions step by step:

1. (2y - x)^2: Expanding the expression: (2y - x)^2 = (2y - x)(2y - x) = 4y^2 - 2xy - 2xy + x^2 = 4y^2 - 4xy + x^2

2. (2xy + 3y)^2: Expanding the expression: (2xy + 3y)^2 = (2xy + 3y)(2xy + 3y) = 4x^2y^2 + 6xy^2 + 6xy^2 + 9y^2 = 4x^2y^2 + 12xy^2 + 9y^2

3. (3x - 1)^3: Expanding the expression: (3x - 1)^3 = (3x - 1)(3x - 1)(3x - 1) = (9x^2 - 3x - 3x + 1)(3x - 1) = (9x^2 - 6x + 1)(3x - 1) = 27x^3 - 18x^2 + 3x - 3x^2 + 2x - 1 = 27x^3 - 21x^2 + 5x - 1

4. a^2 - 81/B: The expression is not fully specified. Please provide the values of 'a' and 'B' so that I can solve it.

5. (4x - y)(4x + y): This is the difference of squares. Expanding the expression: (4x - y)(4x + y) = 16x^2 - 4xy + 4xy - y^2 = 16x^2 - y^2

If you have the values for 'a' and 'B' in expression 4, feel free to provide them, and I can help you solve it as well.