Question

Розкладіть на множники на фото завдання

Answer 1

$\displaystyle\bf\\1)\\\\mp^{2} -mq^{2} =m\cdot(p^{2} -q^{2} )=m\cdot(p-q)\cdot(p+q)\\\\2)\\\\20a^{2} -5=5\cdot(4a^{2} -1)=5\cdot\Big[(2a)^{2} -1^{2} \Big]=5\cdot(2a-1)\cdot(2a+1)\\\\3)\\\\c -c^{3} =c\cdot(1-c^{2})=c\cdot(1-c)\cdot(1+c)\\\\4)\\\\64a^{2} - a^{4} =a^{2} \cdot(64-a^{2} )=a^{2} \cdot(8^{2} -a^{2} )=a^{2} \cdot(8-a)\cdot(8+a)\\\\5)\\\\5x^{2} -10xy+5y^{2} =5\cdot(x^{2} -2xy+y^{2})=5\cdot(x-y)^{2} =\\\\=5\cdot(x-y)\cdot(x-y)\\\\6)$

$\displaystyle\bf\\2b+4bn+2bn^{2} =2b\cdot(1+2n+n^{2} )=2b\cdot(1+n)^{2} =\\\\=2b\cdot(1+n)\cdot(1+n)$