Đáp án:
$1)E=\dfrac{37}{4}\\ 2)A=135\\ B=-\dfrac{4}{5}\\ C=4\\ D=-7.$
Giải thích các bước giải:
$1)\\ E=x(x-y)+y(x+y)=x^2-xy+xy+y^2=x^2+y^2\\ x=-\dfrac{1}{2};y=3 \Rightarrow \left(-\dfrac{1}{2}\right)^2+3^2=\dfrac{1}{4}+9=\dfrac{37}{4}\\ 2)\\ A=5x(4x^2-2x+1)-2x(10x^2-5x-2)\\ =20x^3-10x^2+5x-20x^3+10x^2+4x\\ =9x\\ x=15 \Rightarrow A=9.15=135\\ B=5x(x-4y)-4y(y-5x)\\ =5x^2-20xy-4y^2+20xy\\ =5x^2-4y^2\\ x=-\dfrac{1}{5};y=-\dfrac{1}{2} \Rightarrow B=5\left(-\dfrac{1}{5}\right)^2-4\left(-\dfrac{1}{2}\right)^2=5.\dfrac{1}{25}-4.\dfrac{1}{4}=\dfrac{1}{5}-1=-\dfrac{4}{5}\\ C=6xy(xy-y^2)-8x^2(x-y^2)-5y^2(x^2-xy)\\ =6x^2y^2-6xy^3-8x^3+8x^2y^2-5x^2y^2+5xy^3\\ =-8x^3+9x^2y^2-xy^3\\ x=\dfrac{1}{2};y=2 \Rightarrow C=-8\left(\dfrac{1}{2}\right)^3+9\left(\dfrac{1}{2}\right)^2.2^2-\dfrac{1}{2}.2^3\\=-8.\dfrac{1}{8}+9.\dfrac{1}{4}.4-\dfrac{1}{2}.8\\=-1+9-4\\=4\\ D=(y^2+2)(y-4)-(2y^2+1)\left(\dfrac{1}{2}y-2\right)\\ =y^3-4y^2+2y-8-\left(y^3-4y^2+\dfrac{1}{2}y-2\right)\\ =y^3-4y^2+2y-8-y^3+4y^2-\dfrac{1}{2}y+2\\ =\dfrac{3}{2}y-6\\ y=-\dfrac{2}{3} \Rightarrow D=-\dfrac{3}{2}.\dfrac{2}{3}-6=-1-6=-7.$
