Lesson Example Discussion Quiz: Class Homework |
Step-5 |
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 \$(2x - 1)(x^2 + 3x - 4) - 2(x + 2)(x - 1)\$. |
|
2 |
Step |
Given expression is |
\$(2x - 1)(x^2 + 3x - 4) - 2(x + 2)(x - 1)\$ |
3 |
Step |
Expanding the first product then after simplification |
\$2x(x^2 + 3x - 4) - 1(x^2 + 3x - 4)\$ \$2x^3 + 6x^2 - 8x - x^2 - 3x + 4\$ \$2x^3 + 5x^2 - 11x + 4\$ |
4 |
Step |
Expanding the second product then after simplification |
\$2(x^2 - x + 2x - 2)\$ \$2x^2 - 2x + 4x - 4\$ \$2x^2 + 2x - 4\$ |
5 |
Hint |
Subtracting the second term from the first and then simplify the expression |
\$(2x^3 + 5x^2 - 11x + 4) - (2x^2 + 2x - 4)\$ \$2x^3 + 5x^2 -11x + 4 - 2x^2 - 2x + 4\$ \$2x^3 + 3x^2 -13x + 8\$ |
6 |
Step |
Therefore, the simplified expression is \$2x^3 + 3x^2 -13x + 8\$. |
|
7 |
Choice.A |
Incorrect because the last term should be + 8, not − 8 |
\$2x^3 + 3x^2 -13x - 8\$ |
8 |
Choice.B |
It’s accurate; it successfully completed the calculations with precision |
\$2x^3 + 3x^2 -13x + 8\$ |
9 |
Choice.C |
Option C is incorrect because it has a negative coefficient for the \$x^2\$ term, which is not present in the simplification |
\$2x^3 - 3x^2 -13x + 8\$ |
10 |
Choice.D |
Incorrect: Because they have different signs for the terms compared to the correct expression |
\$2x^3 + 3x^2 +13x - 8\$ |
11 |
Answer |
Option |
B |
12 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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