Evaluate
\left(3x-2y\right)^{2}
Expand
9x^{2}-12xy+4y^{2}
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9x^{2}+12xy+4y^{2}-8y\left(3x+2y\right)+16y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+2y\right)^{2}.
9x^{2}+12xy+4y^{2}-24yx-16y^{2}+16y^{2}
Use the distributive property to multiply -8y by 3x+2y.
9x^{2}-12xy+4y^{2}-16y^{2}+16y^{2}
Combine 12xy and -24yx to get -12xy.
9x^{2}-12xy-12y^{2}+16y^{2}
Combine 4y^{2} and -16y^{2} to get -12y^{2}.
9x^{2}-12xy+4y^{2}
Combine -12y^{2} and 16y^{2} to get 4y^{2}.
9x^{2}+12xy+4y^{2}-8y\left(3x+2y\right)+16y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+2y\right)^{2}.
9x^{2}+12xy+4y^{2}-24yx-16y^{2}+16y^{2}
Use the distributive property to multiply -8y by 3x+2y.
9x^{2}-12xy+4y^{2}-16y^{2}+16y^{2}
Combine 12xy and -24yx to get -12xy.
9x^{2}-12xy-12y^{2}+16y^{2}
Combine 4y^{2} and -16y^{2} to get -12y^{2}.
9x^{2}-12xy+4y^{2}
Combine -12y^{2} and 16y^{2} to get 4y^{2}.
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