Question

Rhea is solving a math puzzle. To find the solution of the puzzle, she must find the product of two numbers. The first number is the sum of 23 and x, and the second number is 18 less than two times the first number. Which of the following functions represents the product of these two numbers?

Answer 1

The product of two numbers is
`P(x)=2x^2+74x+644`

Explanation:

We are given that The first number is the sum of 23 and x,

First number = 23+x

The second number is 18 less than two times the first number.

Second Number =
`2(23+x)-18`

The product of two numbers :
`(23+x)(2(23+x)-18)`

`(23+x)(46+2x-18)`

`(23+x)(28+2x)`

`2x^2+74x+644`

Let P(x) denotes the product

So, The product of two numbers is
`P(x)=2x^2+74x+644`

Hence Option D is true .

The product of two numbers is
`P(x)=2x^2+74x+644`

Answer 2

First number = 23+x

Second number = 2(23+x)-18 = 46 +2x -18 = 2x +28

Now multiply each term by each term :

23 +x * 2x +28

23 * 2x + 23 * 28 + x *2x + x*28=

46x + 644 + 2x^2 + 28x =

Final answer = 2x^2 +74x +644

The answer is D.