Question

1. Phân tích...nhóm hạng tử:

a) 5x - 5y + ax - ay

b) a³ - a²x - ay + xy

c) 10x² + 10xy + 5x + 5y

d) 5ay - 3bx + ax - 15by

e) x³ + x² - x - 1

f) 2bx - 3ay - 6by + ax

h) x + 2a ( x - y ) - y

Answer 1

\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(5+a\right)\left(x-y\right)\)

\(a^3-a^2x-ay+xy=a^2\left(a-x\right)-y\left(a-x\right)=\left(a^2-y\right)\left(a-x\right)\)

\(10x^2+10xy+5x+5y=10x\left(x+y\right)+5\left(x+y\right)=5\left(2x+1\right)\left(x+y\right)\) \(5ay-3bx+ax-15by=a\left(5y+x\right)-3b\left(5y+x\right)=\left(a-3b\right)\left(5y+x\right)\) \(x^3+x^2-x-1=x^2\left(x+1\right)-\left(x+1\right)=\left(x^2-1\right)\left(x+1\right)=\left(x+1\right)^2\left(x-1\right)\) \(2bx-3ay-6by+ax=x\left(2b+a\right)-3y\left(2b+a\right)=\left(x-3y\right)\left(2b+a\right)\)

\(x+2a\left(x-y\right)-y=\left(x-y\right)+2a\left(x-y\right)=\left(1+2a\right)\left(x-y\right)\)