1. a) (x+4)^2=x^2+8x+16; б) (a-2b)^2=a^2-4ab+4b^2; в)(3у+5)×(3у-5)=9у^2-25.
2. а) (с-2)×(с+3)-(с-1)^2=с^2+с-6-с^2+2с-1=3с-7; б) 3×(а+с)^2-6ас=3×(а^2+2ас+с^2)-6ас=3а^2+6ас+3с^2-6ас=3а^2+3с^2;
3. а) 16а^2-9=(4а-3)×(4а+3); б)3х^3-75х=3х×(х^2-25)=3х×(х-5)×(х+5); в) 2х^2+4ху+2у^2=2×(х^2+2ху+у^2)=2×(х+у)^2; 4. (6х-х^2)^2-х^2×(х-1)×(х+1)+6х×(3+2х^2)=36-12х^3+х^4-х^2×(х^2-1)+18х+12х^3=36-12х^3+х^4-х^4+х^2+18х+12х^3=х^2+18х+36; 5. а) (у+2)^2-4у^2=(у+2)^2-(2у)^2=(у+2-2у)×(у+2+2у)=(2-у)×(2+3у); б) х^3-8у^3=(х-2у)×(х^2+2ху+4у^2); в) 16-х^4/81=(4)^2-(х^2/9)^2=(4-х^2/9)×(4+х^2/9)=(2-х/3)×(2+х/3)×(4+х^2/9); г) 2х+х^2+2у-у^2=2×(х+у)+(х-у)×(х+у)=(х+у)×(2+х-у).