因式分解 m^9n^{15}+p^{21}

解答

因式分解

m^{9} n^{15} + p^{21}

(m^{3} n^{5} + p^{7}) (m^{6} n^{10} - m^{3} n^{5} p^{7} + p^{14})

求解步骤

m^{9} n^{15} + p^{21}

将

m^{9} n^{15}

改写为

(m^{3} n^{5})^{3}

= (m^{3} n^{5})^{3} + p^{21}

使用指数法则:

a^{b c} = (a^{b})^{c}

p^{21} = (p^{7})^{3}

= (m^{3} n^{5})^{3} + (p^{7})^{3}

使用立方和公式:

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

(m^{3} n^{5})^{3} + (p^{7})^{3} = (m^{3} n^{5} + p^{7}) ((m^{3} n^{5})^{2} - p^{7} m^{3} n^{5} + p^{14})

= (p^{7} + m^{3} n^{5}) (p^{14} - p^{7} m^{3} n^{5} + (m^{3} n^{5})^{2})

化简

(m^{3} n^{5} + p^{7}) ((m^{3} n^{5})^{2} - p^{7} m^{3} n^{5} + p^{14}) : (m^{3} n^{5} + p^{7}) (m^{6} n^{10} - m^{3} n^{5} p^{7} + p^{14})

= (m^{3} n^{5} + p^{7}) (m^{6} n^{10} - m^{3} n^{5} p^{7} + p^{14})

f (t) = (sin (t))^{2}

f a c t or (k^{2} + 3 k + 2)^{2}

f a c t or a x - 2 b x + 2 a y - 4 b y

f a c t or x^{2} y - 2 x y + x^{2} + 2 y - 2 x + 2

f a c t or [(x - 5 y) + z] [(x - 5 y) - z]