Question

помогите пожалуйста номер 603

Answer 1

$\displaystyle\bf\\1)\\\\(x-2)^{2} -4=(x-2)^{2} -2^{2} =(x-2-2)\cdot(x-2+2)=x\cdot(x-4)\\\\2)\\\\(b+7)^{2} -100c^{2} =(b+7)^{2} -(10c)^{2} =(b+7-10c)\cdot(b+7+10c)\\\\3)\\\\121-(b+7)^{2} =11^{2} -(b+7)^{2} =(11-b-7)\cdot(11+b+7)=\\\\=(4-b)\cdot(18+b)\\\\4)\\\\a^{4} -(7b-a^{2} )^{2} =(a^{2})^{2} -(7b-a^{2} )^{2} =\\\\=(a^{2} -7b+a^{2})\cdot(a^{2} +7b-a^{2})=7b\cdot(2a^{2}-7b)$

$\displaystyle\bf\\5)\\\\(4x-9)^{2}-( 2x+19)^{2} =(4x-9-2x-19)\cdot(4x-9+2x+19)=\\\\=(2x-28)\cdot(6x+10)=2\cdot(x-14)\cdot 2\cdot(3x+5)=\\\\=4\cdot(x-14)\cdot(3x+5)\\\\6)\\\\(a+b+c)^{2} -(a-b-c)^{2} =\\\\=(a+b+c-a+b+c)\cdot(a+b+c+a-b-c)=\\\\=(2b+2c)\cdot 2a=2\cdot(b+c)\cdot 2a=4a\cdot(b+c)$