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Consider the expressions given below:

A. [tex]\(2x^3 - x^2 - 6x\)[/tex]

B. [tex]\(2x^3 + 8x + 4\)[/tex]

C. [tex]\(3x^4 + x^2 + x - 7\)[/tex]

D. [tex]\(3x^4 - 3x^2 + 5x - 7\)[/tex]

For each expression below, select the letter that corresponds to the equivalent expression from the given list:

1. [tex]\((4x^3 - 4 + 7x) - (2x^3 - x - 8)\)[/tex] is equivalent to expression [tex]\(\square\)[/tex]

2. [tex]\((-3x^2 + x^4 + x) + (2x^4 - 7 + 4x)\)[/tex] is equivalent to expression [tex]\(\square\)[/tex]

3. [tex]\((x^2 - 2x)(2x + 3)\)[/tex] is equivalent to expression [tex]\(\square\)[/tex]

Sagot :

GinnyAnswer
Sure, let's go through the problem step-by-step:

### First Expression
Given Expression: [tex]\((4x^3 - 4 + 7x) - (2x^3 - x - 8)\)[/tex]

1. Distribute the negative sign inside the second parenthesis:
[tex]\[ (4x^3 - 4 + 7x) - 2x^3 + x + 8 \][/tex]

2. Combine like terms:
[tex]\[ (4x^3 - 2x^3) + (7x + x) + (-4 + 8) \][/tex]
[tex]\[ 2x^3 + 8x + 4 \][/tex]

3. The simplified expression matches expression B: [tex]\(2x^3 + 8x + 4\)[/tex].

### Second Expression
Given Expression: [tex]\((-3x^2 + x^4 + x) + (2x^4 - 7 + 4x)\)[/tex]

1. Combine like terms directly:
[tex]\[ x^4 + 2x^4 - 3x^2 + x + 4x - 7 \][/tex]
[tex]\[ 3x^4 - 3x^2 + 5x - 7 \][/tex]

2. The simplified expression matches expression D: [tex]\(3x^4 - 3x^2 + 5x - 7\)[/tex].

### Third Expression
Given Expression: [tex]\((x^2 - 2x)(2x + 3)\)[/tex]

1. Distribute each term in the first parenthesis by each term in the second parenthesis:
[tex]\[ x^2 \cdot 2x + x^2 \cdot 3 - 2x \cdot 2x - 2x \cdot 3 \][/tex]
[tex]\[ 2x^3 + 3x^2 - 4x^2 - 6x \][/tex]

2. Combine like terms:
[tex]\[ 2x^3 - x^2 - 6x \][/tex]

3. The simplified expression matches expression A: [tex]\(2x^3 - x^2 - 6x \)[/tex].

### Final Answers
1. [tex]\((4 x^3 - 4 + 7x) - (2 x^3 - x - 8)\)[/tex] is equivalent to expression B.
2. [tex]\((-3 x^2 + x^4 + x) + (2 x^4 - 7 + 4x)\)[/tex] is equivalent to expression D.
3. [tex]\((x^2 - 2x)(2x + 3)\)[/tex] is equivalent to expression A.

Thus, the answers to the expressions are:
1. B
2. D
3. A
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