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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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Simplify the following expression. (4x + 1)2 − (4x + 3) (4x − 1)a)(4x + 1)b)4c)(4x − 3)d)4xCorrect answer is option 'B'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Simplify the following expression. (4x + 1)2 − (4x + 3) (4x − 1)a)(4x + 1)b)4c)(4x − 3)d)4xCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify the following expression. (4x + 1)2 − (4x + 3) (4x − 1)a)(4x + 1)b)4c)(4x − 3)d)4xCorrect answer is option 'B'. Can you explain this answer?.
Simplify the following expression. (4x + 1)2 − (4x + 3) (4x − 1)a)(4x + 1)b)4c)(4x − 3)d)4xCorrect answer is option 'B'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Simplify the following expression. (4x + 1)2 − (4x + 3) (4x − 1)a)(4x + 1)b)4c)(4x − 3)d)4xCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify the following expression. (4x + 1)2 − (4x + 3) (4x − 1)a)(4x + 1)b)4c)(4x − 3)d)4xCorrect answer is option 'B'. Can you explain this answer?.
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