Lesson Example Discussion Quiz: Class Homework |
Step-1 |
Title: Equivalent expressions |
Grade: 1300-a Lesson: S1-L5 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
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 is |
\$ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \$ |
4 |
Hint |
Applying this formula to our expression, and then simplifying the equation we get |
\$(x^3 - y^3)/(x - y)\$ = \$((x - y)(x^2 + xy + y^2))/((x - y))\$ \$ (x^2 + xy + y^2) \$ |
5 |
Step |
So, the simplified expression is \$ (x^2 + xy + y^2) \$. |
|
6 |
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 |
\$ x^3 + xy + y^3 \$ |
7 |
Choice.B |
Correct: It accurately done the calculation by using the factorization formula |
\$ x^2 + xy + y^2 \$ |
8 |
Choice.C |
\$x^2 + 2xy + y^2\$, is incorrect as it fails to reflect the accurate simplification of the expression without 2xy |
\$ x^2 + 2xy + y^2 \$ |
9 |
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 |
\$ x^2 - xy - y^2 \$ |
10 |
Answer |
Option |
B |
11 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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