Final answer:
The identity a^2 - b^2 = (a + b)(a + b) is false. The correct form of the identity is a^2 - b^2 = (a + b)(a - b), which is called the difference of squares. The given identity mistakenly implies that a^2 - b^2 could be expanded into a complete square, which includes an incorrect middle term 2ab.
Step-by-step explanation:
The identity a^2 - b^2 = (a + b)(a + b) is false. The correct identity should be a^2 - b^2 = (a + b)(a - b). This can be shown by expanding the product on the right side:
(a + b)(a - b) = a2 - ab + ab - b2
Notice that the terms -ab and ab cancel each other out, leaving us with a2 - b2, which is known as the difference of squares.
In contrast, if we were to expand the incorrect product (a + b)(a + b), we would get:
(a + b)(a + b) = a2 + 2ab + b2
Which is clearly not equal to a2 - b2 since it includes the additional term of 2ab.