Question
Real Tutor Solution
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Answer
The simplified form is \( x^{2}-11xy+11y^{2} \).
Solution
Calculate or simplify the expression \( (2x-3y)^2-(x-y)(3x+2y) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2x-3y\right)^{2}-\left(x-y\right)\left(3x+2y\right)\)
- step1: Multiply the terms:
\(\left(2x-3y\right)^{2}+\left(-x+y\right)\left(3x+2y\right)\)
- step2: Expand the expression:
\(4x^{2}-12xy+9y^{2}+\left(-x+y\right)\left(3x+2y\right)\)
- step3: Expand the expression:
\(4x^{2}-12xy+9y^{2}-3x^{2}+xy+2y^{2}\)
- step4: Subtract the terms:
\(x^{2}-11xy+11y^{2}\)
The simplified form of the expression \( (2x-3y)^{2}-(x-y)(3x+2y) \) is \( x^{2}-11xy+11y^{2} \).
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Simplify this solution Beyond the Answer
To simplify the expression \( (2x - 3y)^{2} - (x - y)(3x + 2y) \), let's first expand both parts. Expanding \( (2x - 3y)^{2} \): \[ (2x - 3y)^{2} = 4x^{2} - 12xy + 9y^{2} \] Now, expanding \( (x - y)(3x + 2y) \): \[ (x - y)(3x + 2y) = 3x^{2} + 2xy - 3xy - 2y^{2} = 3x^{2} - xy - 2y^{2} \] Now, substitute the expanded expressions back into the original expression: \[ (4x^{2} - 12xy + 9y^{2}) - (3x^{2} - xy - 2y^{2}) \] Distributing the negative sign: \[ 4x^{2} - 12xy + 9y^{2} - 3x^{2} + xy + 2y^{2} \] Now, combine like terms: \[ (4x^{2} - 3x^{2}) + (-12xy + xy) + (9y^{2} + 2y^{2}) = x^{2} - 11xy + 11y^{2} \] The final simplified expression is: \[ \boxed{x^{2} - 11xy + 11y^{2}} \]
