Question

Complete the following: (2x +5y)(2x − 5y)= ____ - _____

Answer 1

(2x +5y)(2x − 5y) =
`{4x^(2)  - 25y^(2)`

Explanation:

(2x +5y)(2x − 5y) is the given equation.

Now, the ALGEBRAIC IDENTITY states that:

`(a+ b)(a-b) = a^(2)  - b^(2)`

Here, comparing a = 2x and b = 5y,

we get (2x +5y)(2x − 5y) =
`(2x)^(2)  - (5y)^(2)`

on further solving the right side, we get

(2x +5y)(2x − 5y) =
`{4x^(2)  - 25y^(2)`