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Solve the following:
Simplify the following
(x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)?
Simplify the following
(x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)?
Most Upvoted Answer
Solve the following: Simplify the following (x + 3y)(x - 2y) + ( y+ 4x...
Step 1: Expand the Expressions
To simplify the expression (x + 3y)(x - 2y) + (y + 4x)(y - 3x), we start by expanding each part using the distributive property.
- For (x + 3y)(x - 2y):
- x * x = x^2
- x * (-2y) = -2xy
- 3y * x = 3xy
- 3y * (-2y) = -6y^2
Combining these, we get:
- x^2 + (3xy - 2xy) - 6y^2 = x^2 + xy - 6y^2
- For (y + 4x)(y - 3x):
- y * y = y^2
- y * (-3x) = -3xy
- 4x * y = 4xy
- 4x * (-3x) = -12x^2
Combining these, we get:
- y^2 + (4xy - 3xy) - 12x^2 = y^2 + xy - 12x^2
Step 2: Combine the Results
Now, we can put the two expanded expressions together:
- (x^2 + xy - 6y^2) + (y^2 + xy - 12x^2)
Combine like terms:
- x^2 - 12x^2 = -11x^2
- xy + xy = 2xy
- -6y^2 + y^2 = -5y^2
Thus, the combined expression simplifies to:
- -11x^2 + 2xy - 5y^2
Final Simplified Expression
The final simplified expression is:
- -11x^2 + 2xy - 5y^2
This is the simplest form of the original expression.
To simplify the expression (x + 3y)(x - 2y) + (y + 4x)(y - 3x), we start by expanding each part using the distributive property.
- For (x + 3y)(x - 2y):
- x * x = x^2
- x * (-2y) = -2xy
- 3y * x = 3xy
- 3y * (-2y) = -6y^2
Combining these, we get:
- x^2 + (3xy - 2xy) - 6y^2 = x^2 + xy - 6y^2
- For (y + 4x)(y - 3x):
- y * y = y^2
- y * (-3x) = -3xy
- 4x * y = 4xy
- 4x * (-3x) = -12x^2
Combining these, we get:
- y^2 + (4xy - 3xy) - 12x^2 = y^2 + xy - 12x^2
Step 2: Combine the Results
Now, we can put the two expanded expressions together:
- (x^2 + xy - 6y^2) + (y^2 + xy - 12x^2)
Combine like terms:
- x^2 - 12x^2 = -11x^2
- xy + xy = 2xy
- -6y^2 + y^2 = -5y^2
Thus, the combined expression simplifies to:
- -11x^2 + 2xy - 5y^2
Final Simplified Expression
The final simplified expression is:
- -11x^2 + 2xy - 5y^2
This is the simplest form of the original expression.
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Solve the following: Simplify the following (x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)?
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Solve the following: Simplify the following (x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Solve the following: Simplify the following (x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following: Simplify the following (x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)?.
Solve the following: Simplify the following (x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Solve the following: Simplify the following (x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following: Simplify the following (x + 3y)(x - 2y) + ( y+ 4x)(y- 3x)?.
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