展开 (x+y)(x-y)(x^2+xy+y^2)(x^2-xy+y^2)

解答

展开

(x + y) (x - y) (x^{2} + x y + y^{2}) (x^{2} - x y + y^{2})

x^{6} + x^{4} y^{2} - x^{3} y^{3} + 2 x^{2} y^{4} - y^{2} x^{4} + y^{3} x^{3} - 2 y^{4} x^{2} - y^{6}

求解步骤

(x + y) (x - y) (x^{2} + x y + y^{2}) (x^{2} - x y + y^{2})

Apply Difference of Two Squares

(x + y) (x - y) : x^{2} - y^{2}

= (x^{2} - y^{2}) (x^{2} + x y + y^{2}) (x^{2} - x y + y^{2})

展开

(x^{2} - y^{2}) (x^{2} + x y + y^{2}) : x^{4} + x^{3} y + x^{2} y^{2} - y^{2} x^{2} - x y^{3} - y^{4}

= (x^{4} + x^{3} y + x^{2} y^{2} - y^{2} x^{2} - x y^{3} - y^{4}) (x^{2} - x y + y^{2})

打开括号

= x^{4} x^{2} + x^{4} (- x y) + x^{4} y^{2} + x^{3} y x^{2} + x^{3} y (- x y) + x^{3} y y^{2} + x^{2} y^{2} x^{2} + x^{2} y^{2} (- x y) + x^{2} y^{2} y^{2} - y^{2} x^{2} x^{2} - y^{2} x^{2} (- x y) - y^{2} x^{2} y^{2} - x y^{3} x^{2} - x y^{3} (- x y) - x y^{3} y^{2} - y^{4} x^{2} - y^{4} (- x y) - y^{4} y^{2}

化简

x^{4} x^{2} + x^{4} (- x y) + x^{4} y^{2} + x^{3} y x^{2} + x^{3} y (- x y) + x^{3} y y^{2} + x^{2} y^{2} x^{2} + x^{2} y^{2} (- x y) + x^{2} y^{2} y^{2} - y^{2} x^{2} x^{2} - y^{2} x^{2} (- x y) - y^{2} x^{2} y^{2} - x y^{3} x^{2} - x y^{3} (- x y) - x y^{3} y^{2} - y^{4} x^{2} - y^{4} (- x y) - y^{4} y^{2} : x^{6} + x^{4} y^{2} - x^{3} y^{3} + 2 x^{2} y^{4} - y^{2} x^{4} + y^{3} x^{3} - 2 y^{4} x^{2} - y^{6}

= x^{6} + x^{4} y^{2} - x^{3} y^{3} + 2 x^{2} y^{4} - y^{2} x^{4} + y^{3} x^{3} - 2 y^{4} x^{2} - y^{6}

s im pl i f y (4 p^{2} \cdot 2 q - 3 r - 6)^{- 3}

s im pl i f y 2 x - 5 x - x + 2 x

s im pl i f y \frac{3}{2} e^{x} - \frac{2}{2} e^{x}

s im pl i f y \frac{( a ^{2} - 5 )}{( a - 5 )}

s im pl i f y (a - b) (a^{2} + b^{2}) + (a + b) (a^{2} - b^{2})