Question

1.Scoateti factorul comun: a.) 5x(x+2) + (x+2)la puterea a 2 in continuare minus 3(x+2)
b.) (x+1)(x+2)+4(x+1)la puterea a2 minus 4x(x+1)
c.)(x+2)(3x-7)-(x+2)(4x+2)+3(x+2)
d.)(2x-1)laputera a 2 minus (3x+2)(2x-1)+6x(2x-1)
e.)(5x-4)(3x-2) la puterea a doua minus (3x-2)la puterea 3+2(x+4)(3x-2) la puterea a doua .

Answer 1

a. 5x(x+2)+(x+2)²-3(x+2)=(x+2)[5x+(x+2)-3]=(x+2)(5x+x+2-3)=(x+2)(6x-1)
b. (x+1)(x+2)+4(x+1)²-4x(x+1)=(x+1)[(x+2)+4(x+1)-4x]=(x+1)(x+2+4x+4-4x)=
=(x+1)(x+6)
c. (x+2)[(3x-7)-(4x+2)+3]=(x+2)(3x-7-4x-2+3)=(x+2)(-x-6)=-(x+2)(x+6)
d. (2x-1)²-(3x+2)(2x-1)+6x(2x-1)=(2x-1)[(2x-1)-(3x+2)+6x]=
=(2x-1)(2x-1-3x-2+6x)=(2x-1)(5x-3)
e. (5x-4)(3x-2)²-(3x-2)³+2(x+4)(3x-2)²=(3x-2)²[(5x-4)-(3x-2)+2(x+4)]=
=(3x-2)²(5x-4-3x+2+2x+8)=(3x-2)²(4x+6)=2(3x-2)²(2x+3)