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\frac{\left(3x-2y\right)^{2}}{2^{2}}-\left(\frac{3x+2y}{2}\right)^{2}
To raise \frac{3x-2y}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(3x-2y\right)^{2}}{2^{2}}-\frac{\left(3x+2y\right)^{2}}{2^{2}}
To raise \frac{3x+2y}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(3x-2y\right)^{2}}{2^{2}}-\frac{\left(3x+2y\right)^{2}}{4}
Calculate 2 to the power of 2 and get 4.
\frac{\left(3x-2y\right)^{2}}{4}-\frac{\left(3x+2y\right)^{2}}{4}
To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.
\frac{\left(3x-2y\right)^{2}-\left(3x+2y\right)^{2}}{4}
Since \frac{\left(3x-2y\right)^{2}}{4} and \frac{\left(3x+2y\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.
\frac{9x^{2}-12xy+4y^{2}-9x^{2}-12xy-4y^{2}}{4}
Do the multiplications in \left(3x-2y\right)^{2}-\left(3x+2y\right)^{2}.
\frac{-24xy}{4}
Combine like terms in 9x^{2}-12xy+4y^{2}-9x^{2}-12xy-4y^{2}.
-6xy
Divide -24xy by 4 to get -6xy.
\frac{\left(3x-2y\right)^{2}}{2^{2}}-\left(\frac{3x+2y}{2}\right)^{2}
To raise \frac{3x-2y}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(3x-2y\right)^{2}}{2^{2}}-\frac{\left(3x+2y\right)^{2}}{2^{2}}
To raise \frac{3x+2y}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(3x-2y\right)^{2}}{2^{2}}-\frac{\left(3x+2y\right)^{2}}{4}
Calculate 2 to the power of 2 and get 4.
\frac{\left(3x-2y\right)^{2}}{4}-\frac{\left(3x+2y\right)^{2}}{4}
To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.
\frac{\left(3x-2y\right)^{2}-\left(3x+2y\right)^{2}}{4}
Since \frac{\left(3x-2y\right)^{2}}{4} and \frac{\left(3x+2y\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.
\frac{9x^{2}-12xy+4y^{2}-9x^{2}-12xy-4y^{2}}{4}
Do the multiplications in \left(3x-2y\right)^{2}-\left(3x+2y\right)^{2}.
\frac{-24xy}{4}
Combine like terms in 9x^{2}-12xy+4y^{2}-9x^{2}-12xy-4y^{2}.
-6xy
Divide -24xy by 4 to get -6xy.