Question

Replace * with a monomial so that the expression represents the square of a binomial. *+24x+9

Answer 1

`*+24x+9 = 16x^2 + 24x + 9`

Explanation:

Given

`* + 24x + 9`

Required

Fill in the gap

`* + 24x + 9`

Express 24x as a sum of equal halves

`* + 12x + 12x + 9`

Group into two

`(* + 12x) + (12x + 9)`

Factorize 12x + 9

`(* + 12x) + 3(4x + 3)`

Ignore the incomplete part and focus on (4x + 3)

Since the binomial is a square, then the factors of the binomial are :

(4x + 3) and (4x + 3)

So, we have:

`(* + 12x) + 3(4x + 3) = (4x + 3)(4x + 3)`

Expand

`(* + 12x) + 3(4x + 3) = 16x^2 + 12x + 12x + 9`

`(* + 12x) + 3(4x + 3) = 16x^2 + 24x + 9`

Hence:

`*+24x+9 = 16x^2 + 24x + 9`