Question

розкладіть на множники:
1) а^5-a^3 =
2)28-7x^2=
3)a^5-a^3b^2=
4) 3x^2+6xy+3y^2=
5)-4b^2+8ba-4a^2=
6)a^5+6a^4m+9a^3m^2=
7) 2ax^2+4ax+2a=

Answer 1

$\displaystyle\bf\\1)\\\\a^{5} - a^{3} =a^{3} \cdot(a^{2} -1)=a^{3} \cdot(a-1)\cdot(a+1)\\\\2)\\\\28-7x^{2} =7\cdot(4-x^{2} )=7\cdot(2^{2} -x^{2} )=\\\\=7\cdot(2-x)\cdot(2+x)\\\\3)\\\\a^{5} -a^{3} b^{2} =a^{3} \cdot(a^{2} -b^{2} )=a^{3} \cdot(a-b)\cdot(a+b)\\\\4)\\\\3x^{2} +6xy+3y^{2} =3\cdot(x^{2} +2xy+y^{2} )=\\\\=3\cdot(x+y)^{2}=3\cdot(x+y)\cdot(x+y)$

$\displaystyle\bf\\5)\\\\-4b^{2} +8ba-4a^{2} =-4\cdot(b^{2} -2ba+a^{2} )=\\\\=-4\cdot(b-a)^{2} =-4\cdot(b-a)\cdot(b-a)\\\\6)\\\\a^{5} +6a^{4} m+9a^{3} m^{2} =a^{3} \cdot(a^{2}+6am+9m^{2})=\\\\=a^{3} \cdot(a+3m)^{2}= a^{3} \cdot(a+3m)\cdot(a+3m)\\\\7)\\\\2ax^{2} +4ax+2a=2a\cdot(x^{2} +2x+1)=\\\\=2a\cdot(x+1)^{2} =2a\cdot(x+1)\cdot(x+1)$