Đáp án:
\(a,\ (5x^2+9xy-2y^2):(x+2y)=5x-y\\ b,\ (x^4-x^3y+x^2y^2-xy^3):(x^2+y^2)=x^2-xy\\ c,\ (4x^5+3xy^4-y^5+2x^4y-6x^3y^2):(2x^3+y^3-2xy^2)=2x^2+xy-y^2\\ d,\ (2a^3+7ab^2-7a^2b-2b^3):(2a-b)=a^2-3ab+2b^2\)
Giải thích các bước giải:
\(a,\ (5x^2+9xy-2y^2):(x+2y)\\ =\dfrac{5x^2+10xy-xy-2y^2}{x+2y}\\ =\dfrac{5x(x+2y)-y(x+2y)}{x+2y}\\ =\dfrac{(x+2y)(5x-y)}{x+2y}\\ =5x-y\\ b,\ (x^4-x^3y+x^2y^2-xy^3):(x^2+y^2)\\ =\dfrac{(x^4+x^2y^2)-(x^3y+xy^3)}{x^2+y^2}\\ =\dfrac{x^2(x^2+y^2)-xy(x^2+y^2)}{x^2+y^2}\\ =\dfrac{(x^2+y^2)(x^2-xy)}{x^2+y^2}\\ =x^2-xy\\ c,\ (4x^5+3xy^4-y^5+2x^4y-6x^3y^2):(2x^3+y^3-2xy^2)\\ =\dfrac{4x^5+(2x^2y^3-2x^2y^3)-4x^3y^2-2x^3y^2+2x^4y+xy^4+2xy^4-y^5}{2x^3+y^3-2xy^2}\\ =\dfrac{(4x^5+2x^2y^3-4x^3y^2)+(2x^4y+xy^4-2x^2y^3)-(2x^3y^2+y^5-2xy^4)}{2x^3+y^3-2xy^2}\\ =\dfrac{2x^2(2x^3+y^3-2xy^2)+xy(2x^3+y^3-2xy^2)-y^2(2x^3+y^3-2xy^2)}{2x^3+y^3-2xy^2}\\ =\dfrac{(2x^3+y^3-2xy^2)(2x^2+xy-y^2)}{2x^3+y^3-2xy^2}\\ =2x^2+xy-y^2\\ d,\ (2a^3+7ab^2-7a^2b-2b^3):(2a-b)\\ =\dfrac{2a^3+3ab^2+4ab^2-a^2b-6a^2b-2b^3}{2a-b}\\ =\dfrac{(2a^3-a^2b)-(6a^2b-3ab^2)+(4ab^2-2b^3)}{2a-b}\\ =\dfrac{a^2(2a-b)-3ab(2a-b)+2b^2(2a-b)}{2a-b}\\ =\dfrac{(2a-b)(a^2-3ab+2b^2)}{2a-b}\\ =a^2-3ab+2b^2\)
chúc bạn học tốt!
