Đáp án:
$a)M=294\\ b)N=-113\\ c)P=-35\\ d)Q=9\\ e)R=54\\ f)S=18189$
Giải thích các bước giải:
$a)M=x^3-3xy(x-y)-y^3-x^2+2xy-y^2\\ =x^3-3x^2y+3xy^2-y^3-(x^2-2xy+y^2)\\ =(x-y)^3-(x-y)^2\\ =7^3-7^2\\ =294\\ b)N=x^2(x+1)-y^2(y-1)+xy-3xy(x-y+1)-95\\ =x^3+x^2-y^3+y^2+xy-3x^2y+3xy^2-3xy-95\\ =x^3-3x^2y+3xy^2-y^3+x^2-2xy+y^2-95\\ =(x-y)^3+(x-y)^2-95\\ =(-3)^3+(-3)^2-95\\ =-113\\ c)P=3x^2-2x+3y^2-2y+6xy-100\\ =3x^2+6xy+3y^2-2x-2y-100\\ =3(x^2+2xy+y^2)-2(x+y)-100\\ =3(x+y)^2-2(x+y)-100\\ =3.5^2-2.5-100\\ =-35\\ d)Q=x^3+y^3\\ =(x+y)(x^2-xy+y^2)\\ =(x+y)\left(-\dfrac{x^2}{2}-xy-\dfrac{y^2}{2}+\dfrac{3x^2}{2}+\dfrac{3y^2}{2}\right)\\ =(x+y)\left(-\dfrac{1}{2}(x^2+2xy+y^2)+\dfrac{3}{2}(x^2+y^2)\right)\\ =(x+y)\left(-\dfrac{1}{2}(x+y)^2+\dfrac{3}{2}(x^2+y^2)\right)\\ =3\left(-\dfrac{1}{2}.3^2+\dfrac{3}{2}.5\right)\\ =9\\ e)R=x^3-y^3\\ =(x-y)(x^2+xy+y^2)\\ =(x-y)\left(-\dfrac{x^2}{2}+xy-\dfrac{y^2}{2}+\dfrac{3x^2}{2}+\dfrac{3y^2}{2}\right)\\ =(x-y)\left(-\dfrac{1}{2}(x^2-2xy+y^2)+\dfrac{3}{2}(x^2+y^2)\right)\\ =(x-y)\left(-\dfrac{1}{2}(x-y)^2+\dfrac{3}{2}(x^2+y^2)\right)\\ =3\left(-\dfrac{1}{2}.3^2+\dfrac{3}{2}.15\right)\\ =54\\ f)S=(2a+2b-c)^2+(2b+2c-a)^2+(2c+2a-b)^2\\ =(2a+2b-c)(2a+2b-c)+(2b+2c-a)(2b+2c-a)+(2c+2a-b)(2c+2a-b)\\ =4a^2+8ab−4ac+4b^2−4bc+c^2+a^2−4ab−4ac+4b^2+8bc+4c^2+4a^2−4ab+8ac+b^2−4bc+4c^2\\ =9a^2+9b^2+9c^2\\ =9(a^2+b^2+c^2)\\ =9.2021\\ =18189$
