14
a)(5+x)^2+(x-5)^2=
5^2+2*5*x+x^2+(x^2-2*x*5+5^2)=
25+10x+x^2+x^2-10x+25=
2x^2+50
b)(2x+3y)^2+(2x-3y)^2=
(2x)^2+2*2x*3y+(3y)^2+[(2x)^2-2*2x*3y+(3y)^2]=
4x^2+12xy+9y^2+(4x^2-12xy+9y^2)=
4x^2+12xy+9y^2+4x^2-12xy+9y^2=
8x^2+18y^2
18
a)(a+1)^3-2(a-1)^3+(a-1)(a^2+a+1)=
a^3+3*a^2*1+3*a*1^2+1^3-2(a^3+3*a^2*1-3*a*1^2+1^3)+(a^3-a^2+a-a^2-a-1)=
a^3+3a^2+3a+1-2a^3-6a^2+6a-2+a^3-2a^2-1=
-a^2+9a-2
b)(a-1)^3-2(a+1)^3+(a+1)(a^2-a+1)=
a^3+3*a^2*1-3*a*1^2+1^3-2(a^3+3*a^2*1-3*a*1^2+1^3)+(a^3-a^2+a+a^2-a+1)=
a^3+3a^2-3a+1-2a^3-6a^2+6a-2+a^3-a^2+a+a^2-a+1=
a^2+3a
