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y^{2}-4y+4-\left(3y\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-2\right)^{2}.
y^{2}-4y+4-3^{2}y^{2}
Expand \left(3y\right)^{2}.
y^{2}-4y+4-9y^{2}
Calculate 3 to the power of 2 and get 9.
-8y^{2}-4y+4
Combine y^{2} and -9y^{2} to get -8y^{2}.
y^{2}-4y+4-\left(3y\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-2\right)^{2}.
y^{2}-4y+4-3^{2}y^{2}
Expand \left(3y\right)^{2}.
y^{2}-4y+4-9y^{2}
Calculate 3 to the power of 2 and get 9.
-8y^{2}-4y+4
Combine y^{2} and -9y^{2} to get -8y^{2}.