4.
a) b=15 ac=1 1=1*1 rezulta a=c=1
ab+bc+ca=b(a+c)+ca=15(1+1)+1=31
b) c=101 ab=101 101=1*101 a=1 b=101 sau a=101 b=1 a+b=101+1=102
ab+bc+ca=ab+c(b+a)=101+101(101+1)=101+10302=10403
c)a=1 b+c=1 b=0 si c=1 sau b=1 c=0 deci bc=0
ab+bc+ca=a(b+c)+bc=1*1+0=2
5.
a)15a²x+45a²x²-30ax=15ax(a+3ax-2)=
b)43x²-86a²x+43x³=43x(x-2a²+x)
c)2√3x³-4√3x²+16√3x⁵=2√3x²(x-2+8x³)
d)(m+n)+8a(m+n)-2x²(m+n)=(m+n)(1+8a-2x²)
6.
a)10a+b+10b+a=11a+11b=11(a+b) deci divizibil cu 11
b)100a+10b+c+100b+10c+a+100c+10a+b=111a+111b+111c=111(a+b+c)=
=3*37*(a+b+c) deci divizibil cu 37
7.
a)3(a+b)-x(a+b)=(a+b)(3-x)
b)a(m+n)²-b(m+n)²=(m+n)²(a-b)
c)a²(x²+y²)+b²(x²+y²)=(x²+y²)(a²+b²)
d)2m(2m-1)³-(2m-1)³=(2m-1)³(2m-1)=(2m-1)⁴
8.
a)(x+1)(x+2)+(x+2)(x+3)=(x+2)(x+1+x+3)=(x+2)(2x+4)=2(x+2)(x+2)=2(x+2)²
b)a(a+b)-(2a-1)(a+b)=(a+b)(a-2a+1)=(a+b)(1-a)
c)x(3x²+2)+2x(2+3x²)=(3x²+2)(x+2x)=3x*(3x²+2)
d)(2x-3)²-5x(2x-3)=(2x-3)(2x-3-5x)=(2x-3)(-3x-3)=-3*(2x-3)(x+1)
