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

Step

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

Solution

Therefore, the simplified expression is \$2x^3 + 3x^2 -13x + 8\$ .

7

Sumup

Please summarize steps

Choices

8

Choice-A

Incorrect because the last term should be +8, not −8

Wrong \$2x^3 + 3x^2 -13x - 8\$

9

Choice-B

It’s accurate; it successfully completed the calculations with precision

Correct \$2x^3 + 3x^2 -13x + 8\$

10

Choice-C

Option C is incorrect because it has a negative coefficient for the \$x^2\$ term, which is not present in the simplification

Wrong \$2x^3 - 3x^2 -13x + 8\$

11

Choice-D

Incorrect: Because they have different signs for the terms compared to the correct expression

Wrong \$2x^3 + 3x^2 +13x - 8\$

12

Answer

Option

B

13

Sumup

Please summarize choices