1

Problem

Simplify the expression \$(x^3 - y^3)/(x - y)\$.

2

Step

The given expression is

\$(x^3 - y^3)/(x - y)\$

3

Formula

The factorization formula is \$ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \$.

4

Step

Applying this formula to our expression, and then simplifying the equation:

\$(x^3 - y^3)/(x - y) = ((x - y)(x^2 + xy + y^2))/(x - y)\$

\$ (x^2 + xy + y^2) \$

5

Solution

So, the simplified expression is \$ (x^2 + xy + y^2) \$.

6

Sumup

Please summarize steps

Choices

7

Choice-A

It represented by \$x^3 + xy + y^3\$, is inaccurate as it doesn’t align with the simplified expression after canceling x−y

Wrong \$ x^3 + xy + y^3 \$

8

Choice-B

Correct: It accurately done the calculation by using the factorization formula

Correct \$ x^2 + xy + y^2 \$

9

Choice-C

\$x^2 + 2xy + y^2\$, is incorrect as it fails to reflect the accurate simplification of the expression without 2xy

Wrong \$ x^2 + 2xy + y^2 \$

10

Choice-D

Simplifies to \$x^2 + xy + y^2\$, contrasting with the incorrect \$x^2 - xy - y^2\$, as it subtracts xy instead of adding it

Wrong \$ x^2 - xy - y^2 \$

11

Answer

Option

B

12

Sumup

Please summarize choices