Answer :
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]
### 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]
