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8y^{2}+12yx-5x\left(x^{2}+y\right)
Use the distributive property to multiply 4y by 2y+3x.
8y^{2}+12yx-5x^{3}-5xy
Use the distributive property to multiply -5x by x^{2}+y.
8y^{2}+7yx-5x^{3}
Combine 12yx and -5xy to get 7yx.
8y^{2}+12yx-5x\left(x^{2}+y\right)
Use the distributive property to multiply 4y by 2y+3x.
8y^{2}+12yx-5x^{3}-5xy
Use the distributive property to multiply -5x by x^{2}+y.
8y^{2}+7yx-5x^{3}
Combine 12yx and -5xy to get 7yx.