Question

<p>Представте в виде произведения:</p> <p> </p> <p>a) (2x+y)2-(x-2y)2 б) (a+b)2-(b+c)2 в) (m+n)2-(m-n)2 г) p2-(2p+1)2</p> <p>Д) (5с-3d)2-9d2 e) a4-(9b+a2)2</p>

Answer 1

 

$(2x+y)^2-(x-2y)^2=((2x+y)-(x-2y))((2x+y)+ \ +(x-2y))=(2x+y-x+2y)(2x+y+x-2y)= \ =(x+3y)(3x-y) \ (a+b)^2-(b+c)^2=(a+b-b-c)(a+b+b+c)= \ (a-c)(a+2b+c) \ (m+n)^2-(m-n)^2=(m+n-m+n)(m+n+m-n)= \ =2ncdot2m=4mn \ p^2-(2p+1)^2=(p-2p-1)(p+2p+1)=(-p-1)(3p+1)= \ =-(p+1)(3p+1) \ (5c-3d)^2-9d^2= (5c-3d)^2-(3d)^2=(5c-3d-3d)times \ times(5c-3d+3d)= 5c(5c-6d) \ a^4-(9b+a^2)^2=(a^2)^2-(9b+a^2)^2=(a^2-9b-a^2)times \ time(a^2+9b+a^2)=-9b(2a^2+9b)$