Question

Розложите на множители:
1)x^6-y^9
2) 1000a^12b^3+0.001c^9b^15

Answer 1

$1)~x^6-y^9=(x^3+y^{4,5})(x^3-y^{4,5}) \\ 2)~1000a^{12}b^3+0,001c^9d^{15}=10^3a^{12}b^3+10^{-3}c^9d^{15}= \\ =10^{-3}(10^6a^{12}b^3+c^9d^{15})$

Answer 2

$1) x^{6} -y ^{9} = (x^{3} ) ^{2} -(y ^{4.5} ) ^{2} = \\ \\ =( x^{3} -y ^{4.5} )( x^{3} +y ^{4.5})$

$2)1000a ^{12} b ^{3} +0.001c ^{9} b ^{15} = \\ \\=10 ^{3} a ^{12} b ^{3} +10 ^{-3} c ^{9} b ^{15} = \\ \\ =10 ^{-3} (10 ^{6} a ^{12} b ^{3} +c ^{9} b ^{15} )= \\ \\ =10 ^{-3}*b ^{3} (10 ^{6} a ^{12} +c ^{9} b ^{12} )$