Question

Which of the following is/are identities?

• A. $6x+1=7$
• B. $(x+3{)}^2=x^2+6x+9$
• C. $(x+3)(x-3)=x^2-9$
• D. $x^2-3x+2=0$

Answer 1

Answer: (B), (C)

$(x+3)(x-3)=x^2-9$

Identities hold true for all values of the variables.
$\left(a\right)x^2-3x+2=0$
$\Rightarrow (x-2)(x-3)=0$
This holds true only for $x=2,3$
So this is not an identity

$\left(b\right)(x+3{)}^2=x^2+6x+9$
This holds true for all values of $x$
So this is an identity

$\left(c\right)6x+1=7$
$\Rightarrow x=1$
This holds true for $x=1$ only.
So this is not an identity

$\left(d\right)(x+3)(x-3)=x^2-9$
This holds true for all values of $x$
So this is an identity