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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
Let’s analyze the given expressions step-by-step and match them with the correct options.

### Step 1: Simplify the first expression
Given expression:
[tex]\[ (4x^3 - 4 + 7x) - (2x^3 - x - 8) \][/tex]

Simplify it:

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

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

So, the simplified expression is [tex]\(2x^3 + 8x + 4\)[/tex]. This corresponds to expression B.

### Step 2: Simplify the second expression
Given expression:
[tex]\[ (-3x^2 + x^4 + x) + (2x^4 - 7 + 4x) \][/tex]

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

So, the simplified expression is [tex]\(3x^4 - 3x^2 + 5x - 7\)[/tex]. This corresponds to expression D.

### Step 3: Expand and simplify the third expression
Given expression:
[tex]\[ (x^2 - 2x)(2x + 3) \][/tex]

Distribute:
[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]
[tex]\[ = 2x^3 - x^2 - 6x \][/tex]

So, the expanded and simplified expression is [tex]\(2x^3 - x^2 - 6x\)[/tex]. This corresponds to expression A.

### Final Selections
[tex]\[ (4x^3 - 4 + 7x) - (2x^3 - x - 8) \text{ is equivalent to expression } B \][/tex]
[tex]\[ (-3x^2 + x^4 + x) + (2x^4 - 7 + 4x) \text{ is equivalent to expression } D \][/tex]
[tex]\[ (x^2 - 2x)(2x + 3) \text{ is equivalent to expression } A \][/tex]

Answers:

[tex]\[ B \quad D \quad A \][/tex]
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