Đáp án:
\(a,\ (2x+4y)^2:(x+2y)-(9x^3-12x^2-3x):(-3x)-3(x^2+3)=8y-10\\ b,\ (13x^2y^2-5x^4+6y^4-13x^3y-13xy^3):(2y^2-x^2-3xy)=5x^2-2xy+3y^2\)
Giải thích các bước giải:
\(a,\ (2x+4y)^2:(x+2y)-(9x^3-12x^2-3x):(-3x)-3(x^2+3)\\ =\left [2(x+2y)\right ]^2:(x+2y)-(-3x^2+4x+1)-3x^2-9\\ =4(x+2y)+3x^2-4x-1-3x^2-9\\ =4x+8y+3x^2-4x-1-3x^2-9\\ =(4x-4x)+8y+(3x^2-3x^2)+(-1-9)\\ =8y-10\\ b,\ (13x^2y^2-5x^4+6y^4-13x^3y-13xy^3):(2y^2-x^2-3xy)\\ =\dfrac{10x^2y^2+6x^2y^2-3x^2y^2-5x^4+6y^4-15x^3y+2x^3y-4xy^3-9xy^3}{2y^2-x^2-3xy}\\ =\dfrac{(10x^2y^2-5x^4-15x^3y)-(4xy^3-2x^3y-6x^2y^2)+(6y^4-3x^2y^2-9xy^3)}{2y^2-x^2-3xy}\\ =\dfrac{5x^2(2y^2-x^2-3xy)-2xy(2y^2-x^2-3xy)+3y^2(2y^2-x^2-3xy)}{2y^2-x^2-3xy}\\ =\dfrac{(2y^2-x^2-3xy)(5x^2-2xy+3y^2)}{2y^2-x^2-3xy}\\ =5x^2-2xy+3y^2\)
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