Final answer:
The statement (a − b)² = a² − b² is false because the correct expanded form of (a − b)² is a² − 2ab + b², which includes the extra term − 2ab that the right side lacks.
Step-by-step explanation:
The statement (a − b)² = a² − b² is false. To demonstrate this, let's expand the left side of the equation using the binomial expansion formula:
(a − b)² = a² − 2ab + b²
As we can see, the expanded form includes an extra term − 2ab, which is not present on the right side of the equation, a² − b². The correct representation of the right side in factored form is a difference of squares:
a² − b² = (a + b)(a − b)
To consider the other parts of the question:
1. The Pythagorean theorem can indeed be used to calculate the length of the resultant vector when two vectors are at right angles to each other. This is because the vectors form a right-angled triangle, and the resultant vector is the hypotenuse. So, this statement is true.
2. For an object moving with constant acceleration, displacement vs. time graph will be a parabola, making this statement true. However, when plotting displacement against time squared, the graph becomes a straight line, so this part is also true.
3. Knowing only the angles of two vectors does not provide enough information to determine the angle of their resultant vector without additional information, thus this statement is false.
Lastly, the commutative property states A + B = B + A for ordinary number addition, which is true.