Question

Розкладіть на множники:
1)-2m^3-2n^3
2)27b-b^4
3)16-a^4
4)1/81p^4-1

Answer 1

$\displaystyle\bf\\1)\\\\-2m^{3} -2n^{3} =-2\cdot(m^{3} +n^{3})=-2\cdot(m+n)\cdot(m^{2}-mn+n^{2})\\\\2)\\\\27b-b^{4} =b\cdot(27-b^{3} )=b\cdot(3^{3}-b^{3} )=b\cdot(3-b)\cdot(9+3b+b^{2} )\\\\3)\\\\16-a^{4} =4^{2} -(a^{2} )^{2} =(4-a^{2} )\cdot(4+a^{2} )=(2-a)\cdot(2+a)\cdot(4+a^{2})\\\\4)\\\\\frac{1}{81} p^{4} -1=\Big(\frac{1}{9} p^{2} \Big)^{2} -1^{2} =\Big(\frac{1}{9} p^{2}-1\Big)\cdot\Big(\frac{1}{9} p^{2} +1\Big)=$

$\displaystyle\bf\\=\Big(\frac{1}{3} p-1\Big)\cdot\Big(\frac{1}{3} p+1\Big)\cdot\Big(\frac{1}{9} p^{2} +1\Big)$