Question

5) 4x (2x - y) - 5y (y - 2x);

Answer 1

4x(2x - y) - 5y(y - 2x) = 8x² - 4xy - 5y² + 10xy = 8x² +6xy - 5y²

Answer 2

To simplify the expression 4x(2x - y) - 5y(y - 2x), you can use the distributive property and then combine like terms. Here's the step-by-step simplification:

1. Distribute the 4x into the expression 2x - y: 4x * 2x - 4x * y

   This simplifies to: 8x^2 - 4xy

2. Distribute the -5y into the expression y - 2x: -5y * y + (-5y) * (-2x)

   This simplifies to: -5y^2 + 10xy

3. Now, combine the two simplified expressions from steps 1 and 2: (8x^2 - 4xy) - (5y^2 - 10xy)

4. Distribute the negative sign into the second expression: 8x^2 - 4xy - 5y^2 + 10xy

5. Combine like terms: (8x^2 - 5y^2) + (-4xy + 10xy)

6. Further simplify by adding/subtracting like terms: 8x^2 - 5y^2 + 6xy

So, the simplified expression is: 8x^2 - 5y^2 + 6xy