化简 (a^4-b^4)/(a-b)

解答

化简

\frac{a ^{4} - b ^{4}}{a - b}

(a^{2} + b^{2}) (a + b)

求解步骤

\frac{a ^{4} - b ^{4}}{a - b}

a^{4} = (a^{2})^{2}

b^{4} = (b^{2})^{2}

= \frac{( a ^{2} ) ^{2} - ( b ^{2} ) ^{2}}{a - b}

使用平方差公式:

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

(a^{2})^{2} - (b^{2})^{2} = (a^{2} + b^{2}) (a^{2} - b^{2})

= \frac{( a ^{2} + b ^{2} ) ( a ^{2} - b ^{2} )}{a - b}

使用平方差公式:

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

a^{2} - b^{2} = (a + b) (a - b)

= \frac{( a ^{2} + b ^{2} ) ( a + b ) ( a - b )}{a - b}

约分:

a - b

= (a^{2} + b^{2}) (a + b)

(z + 1)^{2} = - 49

2 x + 1 < 5 x - 8

f a c t or 2 v^{2} + 20 v + 70

3 x^{2} + 16 < 8 x

\frac{2}{x + 3} > \frac{3}{1 - 4 x}