X²-y²

Question

625a² -81b⁸
4(x-y)² -9(x+y)²

Write the general statement of the expression above

Answer 1

The general statement of the expression above is:

a² - b²

This can be simplified to (a+b)(a-b).

Answer 2

x²-y² = (x+y)(x-y)
625a² -81b⁸ = (25a+9b^4)(25a-9b^4)
4(x-y)² -9(x+y)² = (2(x-y)+3(x+y))(2(x-y)-3(x+y)
= (5x+y)(-x-5y) = -(5x+y)(x+5y)

Answer 3

Thank you for the correction. Here is the correct general statement of the expression above:

x²-y² = (x+y)(x-y)

625a² -81b⁸ = (25a+9b⁴)(25a-9b⁴)

4(x-y)² -9(x+y)² = -(5x+y)(x+5y)