Class 8 Exam > Class 8 Questions > Simplify(xy+yz)2−2x2y2z. Find the value... Start Learning for Free
Simplify(xy + yz)2− 2x2y2z. Find the value when x = -1, y = 1 and z = 2.
- a)4
- b)3
- c)-3
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z ...
Step 1: Simplifying the Expression
To simplify the expression (xy + yz)² - 2x²y²z, we start by expanding (xy + yz)².
- Use the formula (a + b)² = a² + 2ab + b²:
- Here, a = xy and b = yz.
- Expanding gives:
- (xy)² + 2(xy)(yz) + (yz)²
- This results in x²y² + 2xy²z + y²z².
Now, we rewrite the full expression:
- x²y² + 2xy²z + y²z² - 2x²y²z.
Next, we combine like terms:
- Combine the x²y² and -2x²y²z terms:
Final simplified form:
- (x²y² + y²z² + 2xy²z - 2x²y²z).
Step 2: Substituting Values
Now, we substitute x = -1, y = 1, and z = 2 into the simplified expression.
- Substitute:
- x² = (-1)² = 1
- y² = (1)² = 1
- z² = (2)² = 4
Now, substitute into the expression:
- 1(1) + 4 + 2(-1)(1)(2) - 2(1)(-1)²(2)
Calculating each term:
- 1 + 4 + 2(-1)(2) - 2(1)(1)(2)
- = 1 + 4 - 4 - 4
- = 1 + 4 - 8
- = -3.
Final Result
The final value of the expression when x = -1, y = 1, and z = 2 is -3.
Thus, the correct option is C) -3.
To simplify the expression (xy + yz)² - 2x²y²z, we start by expanding (xy + yz)².
- Use the formula (a + b)² = a² + 2ab + b²:
- Here, a = xy and b = yz.
- Expanding gives:
- (xy)² + 2(xy)(yz) + (yz)²
- This results in x²y² + 2xy²z + y²z².
Now, we rewrite the full expression:
- x²y² + 2xy²z + y²z² - 2x²y²z.
Next, we combine like terms:
- Combine the x²y² and -2x²y²z terms:
Final simplified form:
- (x²y² + y²z² + 2xy²z - 2x²y²z).
Step 2: Substituting Values
Now, we substitute x = -1, y = 1, and z = 2 into the simplified expression.
- Substitute:
- x² = (-1)² = 1
- y² = (1)² = 1
- z² = (2)² = 4
Now, substitute into the expression:
- 1(1) + 4 + 2(-1)(1)(2) - 2(1)(-1)²(2)
Calculating each term:
- 1 + 4 + 2(-1)(2) - 2(1)(1)(2)
- = 1 + 4 - 4 - 4
- = 1 + 4 - 8
- = -3.
Final Result
The final value of the expression when x = -1, y = 1, and z = 2 is -3.
Thus, the correct option is C) -3.
Free Test
FREE
| Start Free Test |
Community Answer
Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z ...
(xy + yz)2 - 2x2y2z
Substitute values
Substitute values
= ((-1)(1) + (1)(2))2 - 2(-1)2(1)2(2)
= (-1 + 2)2 - 4
= 1 - 4
= -3
 | Explore Courses for Class 8 exam |  |
Top Courses for Class 8View all
Top Courses for Class 8
Question Description
Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 8. Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free.
Here you can find the meaning of Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Simplify(xy+yz)2−2x2y2z. Find the value when x = -1,y = 1 and z = 2.a)4b)3c)-3d)none of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 8 tests.
| Explore Courses for Class 8 exam | |
Top Courses for Class 8
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
