Question

Допоможіть! Розкласти на множники:
b⁶-4b⁴+12b²-9

Answer 1

$\displaystyle\bf\\b^{6} -4b^{4} +12b^{2} -9=b^{6} -\Big(4b^{4} -12b^{2} +9\Big)=\\\\\\=\Big(b^{3} \Big)^{2} -\Big[(2b^{2} )^{2} -2\cdot 2b^{2} \cdot 3+3^{2} \Big]=\Big(b^{3} \Big)^{2} -\Big(2b^{2} -3\Big)^{2}=\\\\\\=\Big(b^{3} -2b^{2} +3\Big)\cdot\Big(b^{3} +2b^{2} -3\Big)$