Chad was asked whether the following equation is an identity:
(3x + 2y)^2= (3x + 2y)(3x – 2y) + 2(2y)^2 ?
He performed the following steps:
(3x + 2y)
Step 1
= 922 + 4y
Step 2
9r? – 4y + 4y? – 4y
Step 3
(9x² – 44²) + 8y²

The equation is not an identity, because the term 12xy is missing

Step-by-step explanation:

Starting with the expression on the left of the identity, we operate to get an equivalent expression, as follows:

(3x + 2y)² =

= 9x² + 12xy + 4y² =

= 9x² + 12xy + 4y² - 4y² + 4y² =

= 9x² - 4y² + 12xy + 8y² =

= (3x - 2y)(3x + 2y) + 12xy + 2(2y)²

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!