Prove that 3(x + 1)(x + 7) - (2x + 5)^(2) is never positive

Question

Prove that 3(x + 1)(x + 7) -
`(2x + 5)^(2)` is never positive

Answer 1

Answer: The required simplified expression or given expression would never be positive.

Step-by-step explanation:Given that,

To prove that 3(x+1)(x+7)-(2x+5)² is never positive

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

Given expression,

3(x+1)(x+7)-(2x+5)² ,

Simplifying the above expression,

= 3 [x² + 8x + 7] - 4x² - 20x - 25

= 3x² + 8x + 7 - 4x² - 20x -25

= - [x² + 12x + 18]

Since the whole outcome of the simplification is negative so it would never be positive.

Thus, the required simplified expression or given expression both would never be positive.