Question

Which of the following should be set equal to (x+y)(x²−xy+y² ) to form an identity?

A) −3xy+y³
B) x³ +3xy+y³
C) both a and b
D) None of the above

Answer 1

To form an identity, (x+y)(x²−xy+y²) simplifies to x³+y³.

Step-by-step explanation:

To set (x+y)(x²−xy+y²) equal to an identity, we need to multiply and simplify the expression. Let's simplify:

(x+y)(x²−xy+y²)

= x(x²−xy+y²) + y(x²−xy+y²)

= x³−x²y+xy² + x²y−xy²+y³

= x³+y³

So, the expression (x+y)(x²−xy+y²) simplifies to x³+y³. Therefore, the answer is B) x³ + y³.