Question

Jermaine factored several problems as part of his math homework on the difference of two squares. Which of the following problems from Jermaine's homework are incorrectly factored as a difference of two squares? Select ALL that apply.

4x2 - 4x + 1 = (2x+ 1)(2x- 1)
4x2 - 81 = (2x + 9)(2x- 9)
25x2 + 4 = (5x+ 2)(5x- 2)
121 -4x2= （11+2x）（11-2x）

Answer 1

The incorrectly factored problems are 4x^2 - 4x + 1 and 25x^2 + 4 because the first includes a middle term not found in differences of squares, and the second is a sum of squares which cannot be factored over real numbers.

Step-by-step explanation:

The problems incorrectly factored as a difference of two squares from Jermaine's homework are:

• 4x2 - 4x + 1 = (2x+ 1)(2x- 1)
• 25x2 + 4 = (5x+ 2)(5x- 2)

Reasoning:

• The expression 4x2 - 4x + 1 is not a difference of squares because the middle term (-4x) is not present in a standard difference of squares, which has the form a2 - b2. Additionally, the factored form given is incorrect since when expanded it gives 4x2 - 1, not the original trinomial.
• The expression 25x2 + 4 is incorrectly factored as a difference of two squares, as it is actually a sum of two squares, which cannot be factored over the real numbers.