Question

Is p - ap = -ap? Is P -
`(ei)(e1+e2)` P = -
`(ei)(e1+e2)` P?

a) True
b) False

Answer 1

Both expressions in the question, p - ap and P - (ei)(e1+e2)P, are not equivalent to -ap and -(ei)(e1+e2)P respectively, unless 'a' or the term (ei)(e1+e2) equals 1, which is not specified. Thus, the answer to both parts is False.

Step-by-step explanation:

The question essentially asks to verify two algebraic expressions involving subtraction and distribution. The expressions are p - ap and P - (ei)(e1+e2)P. Let's address each expression separately:

• For the first expression, using the distributive property, we can factor out p obtaining p(1 - a). This is not equivalent to -ap unless a = 1, which is not specified. Thus, the correct answer here is b) False.
• For the second expression P - (ei)(e1+e2)P, factoring out P gives us P(1 - (ei)(e1+e2)). This simplifies to P - (ei)(e1+e2)P, which doesn't equal -(ei)(e1+e2)P unless (ei)(e1+e2) equals 1, which, again, is not provided. Thus, this expression is also b) False.

It's important to note that this holds true regardless of whether ei, e1, and e2 are constants, variables, or complex terms. The given mathematical principles apply universally.