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If p and q are two algebraic expression such that p+q=5( x²-2xy+2y²)and p - q = 4xy-x²-2y²,then(3p)=?
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If p and q are two algebraic expression such that p+q=5( x²-2xy+2y²)an...
Given Equations
We start with two equations based on the provided information:
- p + q = 5(x² - 2xy + 2y²)
- p - q = 4xy - x² - 2y²
Step 1: Solve for p and q
To find p and q, we can add and subtract the two equations.
- Adding the equations:
(p + q) + (p - q) = 5(x² - 2xy + 2y²) + (4xy - x² - 2y²)
This simplifies to:
2p = 4x² + 2xy + 3y²
Therefore, p = 2x² + xy + (3/2)y²
- Subtracting the equations:
(p + q) - (p - q) = 5(x² - 2xy + 2y²) - (4xy - x² - 2y²)
This simplifies to:
2q = 6x² - 6xy + 7y²
Hence, q = 3x² - 3xy + (7/2)y²
Step 2: Calculate 3p
Now that we have p, we can find 3p:
- 3p = 3(2x² + xy + (3/2)y²)
Calculating this gives:
- 3p = 6x² + 3xy + (9/2)y²
Final Expression for 3p
Thus, the expression for 3p is:
- 3p = 6x² + 3xy + (9/2)y²
This is the final answer. You can now substitute values for x and y if needed to evaluate further.
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If p and q are two algebraic expression such that p+q=5( x²-2xy+2y²)and p - q = 4xy-x²-2y²,then(3p)=?
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