Simplify the given expression 8(x-2)^(2)+y^(2)-x+y-3xy(1-12 x)=4x(2x-9xy)+(y+9)^(2)-3x(y-7)

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Expand Term 1: Expand the term 8(x-2)² using the formula (a-b)² = a² - 2ab + b². 8(x-2)² = 8(x² - 4x + 4) = 8x² - 32x + 32Expand Term 2: Expand the term (y+9)² using the formula (a+b)² = a² + 2ab + b². (y+9)² = y² + 18y + 81Expand Term 3: Expand the term 3xy(1-12x) by distributing 3xy across the parentheses. 3xy(1-12x) = 3xy - 36x²yExpand Term 4: Expand the term 4x(2x-9xy) by distributing 4x across the parentheses. 4x(2x-9xy) = 8x² - 36x²yCombine Expanded Terms: Combine all the expanded terms into the original equation. 8x² - 32x + 32 + y² - x + y - (3xy - 36x²y) = 8x² - 36x²y + y² + 18y + 81 - 3x(y-7)Simplify Left Side: Simplify both sides of the equation by combining like terms. On the left side: 8x² - 32x + 32 + y² - x + y - 3xy + 36x²y = 8x² - 33x + y² - 2xy + 32 + 36x²y  On the right side: 8x² - 36x²y + y² + 18y + 81 - 3xy + 21x = 8x² - 36x²y + y² + 18y + 81 - 3xy + 21xSimplify Right Side: Subtract 8x², y², and 36x²y from both sides to simplify further. 8x² - 33x + y² - 2xy + 32 + 36x²y - 8x² - y² - 36x²y = 8x² - 36x²y + y² + 18y + 81 - 3xy + 21x - 8x² - y² - 36x²y This simplifies to: -33x - 2xy + 32 = 18y + 81 - 3xy + 21xSubtract Terms: Combine like terms and move all terms to one side to set the equation to zero. -33x - 2xy + 32 - 18y - 81 + 3xy - 21x = 0 This simplifies to: -54x + xy - 18y - 49 = 0Combine and Set to Zero: We have simplified the equation to its simplest form. -54x + xy - 18y - 49 = 0

Simplify the given expression $8(x-2)^{2}+y^{2}-x+y-3xy(1-12x)=4x(2x-9xy)+(y+9)^{2}-3x(y-7)$

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Simplify the given expression 8(x−2)2+y2−x+y−3xy(1−12x)=4x(2x−9xy)+(y+9)2−3x(y−7)8(x-2)^{2}+y^{2}-x+y-3xy(1-12x)=4x(2x-9xy)+(y+9)^{2}-3x(y-7)8(x−2)2+y2−x+y−3xy(1−12x)=4x(2x−9xy)+(y+9)2−3x(y−7)

Simplify the given expression $8(x-2)^{2}+y^{2}-x+y-3xy(1-12x)=4x(2x-9xy)+(y+9)^{2}-3x(y-7)$