Question

Descompuneti :
a) ax+bx+ay+by
b) 5x+5y-ax-ay
c) x+ax+y+ay
d) ax-bx+ax^2-bx^2
e) x^3+x^2-4x-4
f) x^3+x^2+2x+2

Answer 1

a) ax+bx+ay+by=x(a+b)+y(a+b)=(a+b)(x+y)

b)5x+5y-ax-ay=5(x+y)-a(x+y)=(x+y)(5-a)

c) x+ax+y+ay=ax+ay+x+y=a(x+y)+x+y=(x+y)(a+1)

d) ax-bx+ax²-bx²=x(a-b)+x²(a-b)=(a-b)(x+x²)=x(1+x)(a-b)

e) x³+x²-4x-4=x²(x+1)-4(x+1)=(x+1)(x²-4)=(x+1)(x-20(x+2)

f) x³+x²+2x+2=x²(x+1)+2(x+1)=(x+1)(x²+2)