Question

Replace ∗ with a monomial so that the expression can be rewritten as a square of a sum or a difference: 25a² ∗ 1/4b²?

Answer 1

To rewrite the expression as a square of a sum or a difference, we can replace ∗ with (5a - 1/(2b)) and rewrite the expression as (5a - 1/(2b))^2.

Step-by-step explanation:

To rewrite the expression as a square of a sum or a difference, we need to find a monomial that, when squared, gives us 25a² * (1/4b²). One approach is to find the square root of 25a² and the square root of (1/4b²), which are 5a and 1/(2b) respectively. So, a possible monomial to replace ∗ is (5a - 1/(2b)). Now we can rewrite the expression as (5a - 1/(2b))^2.