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Simplify the following expression.
(4x + 1)2 − (4x + 3) (4x − 1)
- a)(4x + 1)
- b)4
- c)(4x − 3)
- d)4x
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Simplify the following expression. (4x + 1)2 − (4x + 3) (4x − 1)a)(4x ...
Formula used
(a + b)2 = a2 + b2 + 2ab
Calculation
(4x + 1)
2
− (4x + 3) (4x − 1)⇒ 16x2 + 1 + 2 × 4x
×
1 - (16x2 - 4x + 12x - 3)⇒
1 + 8x
×
1
- 8x + 3
⇒ 4
The value is 4.
Most Upvoted Answer
Simplify the following expression. (4x + 1)2 − (4x + 3) (4x − 1)a)(4x ...
Simplifying the Expression
To simplify the expression (4x + 1)² − (4x + 3)(4x − 1), we will break it down step by step.
Step 1: Expand the first term
- The expression (4x + 1)² can be expanded using the formula (a + b)² = a² + 2ab + b².
- Here, a = 4x and b = 1. Therefore:
- (4x)² = 16x²
- 2(4x)(1) = 8x
- 1² = 1
- Thus, (4x + 1)² = 16x² + 8x + 1.
Step 2: Expand the second term
- The expression (4x + 3)(4x − 1) uses the distributive property (FOIL method).
- First: (4x)(4x) = 16x²
- Outside: (4x)(-1) = -4x
- Inside: (3)(4x) = 12x
- Last: (3)(-1) = -3
- Combining these gives: 16x² + 8x - 3.
Step 3: Combine both parts
- Now substitute back into the main expression:
- (16x² + 8x + 1) - (16x² + 8x - 3)
- Distributing the negative sign:
- 16x² + 8x + 1 - 16x² - 8x + 3
Step 4: Simplify
- The 16x² and -16x² cancel out.
- The 8x and -8x also cancel out.
- This leaves us with: 1 + 3 = 4.
Conclusion
The simplified expression is 4, which corresponds to option 'B'.
To simplify the expression (4x + 1)² − (4x + 3)(4x − 1), we will break it down step by step.
Step 1: Expand the first term
- The expression (4x + 1)² can be expanded using the formula (a + b)² = a² + 2ab + b².
- Here, a = 4x and b = 1. Therefore:
- (4x)² = 16x²
- 2(4x)(1) = 8x
- 1² = 1
- Thus, (4x + 1)² = 16x² + 8x + 1.
Step 2: Expand the second term
- The expression (4x + 3)(4x − 1) uses the distributive property (FOIL method).
- First: (4x)(4x) = 16x²
- Outside: (4x)(-1) = -4x
- Inside: (3)(4x) = 12x
- Last: (3)(-1) = -3
- Combining these gives: 16x² + 8x - 3.
Step 3: Combine both parts
- Now substitute back into the main expression:
- (16x² + 8x + 1) - (16x² + 8x - 3)
- Distributing the negative sign:
- 16x² + 8x + 1 - 16x² - 8x + 3
Step 4: Simplify
- The 16x² and -16x² cancel out.
- The 8x and -8x also cancel out.
- This leaves us with: 1 + 3 = 4.
Conclusion
The simplified expression is 4, which corresponds to option 'B'.
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Question Description
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