Question

7) Calculati:

A²-(B+C)²
stiind ca:
A=x+2y-3z;
B=2x-3y+z;
C=-3x+y+2z

8) Descompuneti in factori:

a) (x²+3x+1)²-1
b) (2m-3) (m-1)²-4 (2m-3)
c) (p-3) (p²+1)+2p (p-3)
d) (3a-1)²-25
e) (x+2)²-(3-2x)²
f)$(\frac{1}{2} a+\frac{3}{2}b)$²- $(\frac{3}{2} a+\frac{1}{2}b)$²

AJUTOR URGENT!! DAU COROANA SI 20 DE PUNCTE!!

Answer 1

7)
A²-(B+C)² =(A+B+C)(A-B-C)=
=(x+2y-3z+2x-3y+z-3x+y+2z)(x+2y-3z-2x+3y-z+3x-y-2z)=
=0×(2x+4y-6z)=0


8.
a) (x²+3x+1)²-1=(x²+3x+1-1)(x²+3x+1+1)=(x²+3x)(x²+3x+2)=
=x(x+3)(x²+x+2x+2)=x(x+3)[x(x+1)+2(x+1)]=x(x+3)(x+1)(x+2)
b) (2m-3) (m-1)²-4 (2m-3)=(2m-3) [(m-1)²-4 ]=(2m-3)(m-1+2)(m-1-2)=
=(2m-3)(m+1)(m-3)
c) (p-3) (p²+1)+2p (p-3)=(p-3) (p²+1+2p)=(p-3) (p+1)²=
d) (3a-1)²-25=(3a-1-5)(3a-1+5)=(3a-6)(3a+4)
e) (x+2)²-(3-2x)²=(x+2-3+2x)(x+2+3-2x)=(3x-1)(5-x)
f)(a/2+3b/2)²-(3a/2+b/2)²=(a/2+3b/2-3a/2-b/2)(a/2+3b/2+3a/2+b/2)=
=(2b/2-2a/2)(4a/2+4b/2)=(b-a)(2a+2b)=2(b-a)(a+b)