Question

Is this equation an identity? (2x+1)^2-(x+1)^2=3(x+1)^2-1

Answer 1

See below, please

Explanation:

Left side

`{(2x + 1)}^(2) - {(x + 1)}^(2)`

`= (4 {x}^(2) + 4x + 1) - ( {x}^(2) + 2x + 1)`

`= (4 {x}^(2) - {x}^(2) ) + (4x - 2x) + (1 -1 )`

`= 3 {x}^(2) + 2x`

Right side

`3 * {(x + 1)}^(2) - 1`

`= 3 * ( {x}^(2) + 2x + 1) - 1`

`= 3 {x}^(2) + 6x + 3 - 1`

`= 3 {x}^(2) + 6x + 2`

After compared with both sides, we can make a conclusion that

This equation isn't an identity.