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3\left(xy\right)^{2}
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3\left(xy\right)^{2}
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12x^{4}-6x^{3}y+15x^{2}y^{2}-6x^{2}\left(2x^{2}-xy+2y^{2}\right)
Use the distributive property to multiply 3x^{2} by 4x^{2}-2xy+5y^{2}.
12x^{4}-6x^{3}y+15x^{2}y^{2}-12x^{4}+6x^{3}y-12x^{2}y^{2}
Use the distributive property to multiply -6x^{2} by 2x^{2}-xy+2y^{2}.
-6x^{3}y+15x^{2}y^{2}+6x^{3}y-12x^{2}y^{2}
Combine 12x^{4} and -12x^{4} to get 0.
15x^{2}y^{2}-12x^{2}y^{2}
Combine -6x^{3}y and 6x^{3}y to get 0.
3x^{2}y^{2}
Combine 15x^{2}y^{2} and -12x^{2}y^{2} to get 3x^{2}y^{2}.
12x^{4}-6x^{3}y+15x^{2}y^{2}-6x^{2}\left(2x^{2}-xy+2y^{2}\right)
Use the distributive property to multiply 3x^{2} by 4x^{2}-2xy+5y^{2}.
12x^{4}-6x^{3}y+15x^{2}y^{2}-12x^{4}+6x^{3}y-12x^{2}y^{2}
Use the distributive property to multiply -6x^{2} by 2x^{2}-xy+2y^{2}.
-6x^{3}y+15x^{2}y^{2}+6x^{3}y-12x^{2}y^{2}
Combine 12x^{4} and -12x^{4} to get 0.
15x^{2}y^{2}-12x^{2}y^{2}
Combine -6x^{3}y and 6x^{3}y to get 0.
3x^{2}y^{2}
Combine 15x^{2}y^{2} and -12x^{2}y^{2} to get 3x^{2}y^{2}.
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