Question

1,分解因式 （1）x^3-9x (2)6xy^2-9X^2Y-Y^3 (3) (2a-b)^2+8ab 2,已知（x+

Answer 1

1,分解因式 x^3-9x =x*(x^2-9) =x*(x-3)*(x+3) 6xy^2-9X^2Y-Y^3 =Y*(6XY-9X^2-Y^2) =-Y*(9X^2-6XY+Y^2) =-Y*(3X-Y)^2 (2a-b)^2+8ab =4a^2-4ab+b^2+8ab =4a^2+4ab+b^2 =(2a+b)^2 2,已知（x+Y)^2=25,(x-y)^2=9,求xy与x^2+Y^2的值 (x+Y)^2=x^2+2xy+y^2=25 (x-y)^2=X^2-2xy+y^2=9 (x+y)^2-(x-y)^2=4xy=25-9,得到xy=4 (x+y)^2+(x-y)^2=2*(x^2+y^2)=25+9,得到x^2+Y^2=17