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