Question

Descompuneți următoarele expresii în factori ireductibili:
a) x² - 8x + 16;
c) x²+y²+9+2xy + 6x+6y;
b) 9x²+6x+1;
d) x²+4y²+9-4xy+6x-12y;
e) x+3x²+3x+1;
f)x+6x²y+12xy²+8y; h) 8x³-36x²+54xy²-27y³.
g) x-9x²+27x -27y³;


Rapid va roggg !!!!!!!!!

Answer 1

Explicație pas cu pas:

x²-8x+16=(x-4)²

9x²+6x+1=(3x+1)²

x²+y²+9+2xy+6x+6y=x²+y²+2xy+6x+6y+9= =(x+y)²+6(x+y)+9=[(x+y)+3]²=(x+y+3)²

x²+4y²+9-4xy+6x-12y=x²+4y²-4xy+6x-12y+9= =(x-2y)²+6(x-2y)+9=[(x-2y)+3]²=(x-2y+3)²

x+3x²+3x+1=x(3x+1)+3x+1=(3x+1)(x+1)

x+6x²y+12xy²+2y=6x²y+12xy²+x+2y=6xy(x+2y)+x+2y=(x+2y)(6xy+1)

Answer 2

Explicație pas cu pas:

a)

x² - 8x + 16 = x² - 2×4x + 4² = (x - 4)²

b)

9x² + 6x + 1 = (3x)² + 2×3x + 1 = (3x + 1)²

c)

x² + y² + 9 + 2xy + 6x + 6y = (x² + xy + 3x) + (xy + y² + 3y) + (3x + 3y + 9) = x(x + y + 3) + y(x + y + 3) + 3(x + y + 3) = (x + y + 3)²

d)

x² + 4y² + 9 - 4xy + 6x - 12y = x² - 2xy + 3x - 2xy + 4y² - 6y + 3x - 6y + 9 = x(x - 2y + 3) - 2y(x - 2y + 3) + 3(x - 2y + 3) = (x - 2y + 3)²

e)

x+3x²+3x+1 = x(3x + 1) + (3x + 1) = (3x + 1)(x + 1)