1

Problem

Add \$3( 4 (x^3) - 2x^2 + 5x - 3)\$ and \$2( 3x^2) - 6(2x^3) - x + 7\$.

2

Step

The given expressions are

\$3( 4 (x^3) - 2x^2 + 5x - 3)\$ and \$2( 3x^2) - 6(2x^3) - x + 7\$

3

Step

Simplify the expressions

\$12x^3 - 6x^2 + 15x - 9\$ + \$ 6x^2 - 12x^3 - x + 7\$

4

Step

Combine like terms: \$x^3\$

\$12x^3 - 12x^3 = 0\$

5

Step

Terms with \$x^2\$:

\$-6x^2 + 6x^2 = 0\$

6

Step

Terms with x:

\$15x - x = 14x\$

7

Step

Constant terms:

-9 + 7 = -2

8

Step

Write the Simplified Expression

14x - 2

9

Solution

So, the simplified expression is 14x - 2.

10

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

11

Choice-A

14x - 2 is correct because it accurately represents the simplified expression obtained by combining like terms from the expanded forms of the original expressions

Correct 14x - 2

12

Choice-B

This option is incorrect because it includes terms that should not be present after the simplification

Wrong \$12x^3 - 12x^2 - 14x -2\$

13

Choice-C

14x + 2 is incorrect because it has the wrong sign for the constant term

Wrong 14x + 2

14

Choice-D

This option is incorrect because it includes terms that should not be present and has the wrong sign for the constant term

Wrong \$12x^3 + 12x^2 +14x +2\$

15

Step

Option

A

16

Sumup

Please Summarize Choices