Question

descompuneti in factori:
a) 400xy-25y la puterea 2
b)x la puterea 2 -8x-12
c)2x la puterea 2 +4x+8x la puterea 3
d)24x la puterea 2 - 10xy+y la puterea 2
e ) (x la puterea 2 +y+5 ) totul la puterea 2 -(x-5) totul la puterea 2

Answer 1

a) 400xy-25y²=25y(16x-y)
b)x² -8x-12= (x-4-2√7)(x-4+2√7)
Δ=(-8)²+4×1×12=64+48=112
x₁=(8+√112)/2=(8+4√7)/2=4+2√7
x²=(8-√112)/2=(8-4√7)/2=4-2√7

c)2x² +4x+8x³=2x(x +2+4x²)
d)24x² - 10xy+y²=25x² - 10xy+y²-x²=(5x-y)²-x²=(5x-y-x)(5x-y+x)=(4x-y)(6x-y)
e ) (x² +y+5 )² -(x-5)²=[(x² +y+5 -(x-5)][(x² +y+5 +(x-5)]=
=(x² +y+5 -x+5)(x² +y+5 +x-5)=(x² +y -x+10)(x² +y+x)