Question

Phân tích thành nhân tử :

a) \(5x-5y+ax-ay\)

b) \(a^3-a^2x-ay+xy\)

c) \(xy\left(x+y\right)+yz\left(x+z\right)+xz\left(x+z\right)+2xyz\)

Answer 1

a) \(5x-5y+ax-ay\)

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

\(\Leftrightarrow\) \(x\left(5+a\right)-y\left(5+a\right)\)

\(\Leftrightarrow\) \(\left(5+a\right)\left(x-y\right)\)

Answer 2

b) \(a^3-a^2x-ay+xy\)

\(\Leftrightarrow\) \(a^2\left(a-x\right)-y\left(a-x\right)\)

\(\Leftrightarrow\) \(\left(a-x\right)\left(a^2-y\right)\)

Answer 3

c sai chỗ yz(x+z) sửa yz(y+z)

Answer 4

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

b,\(a^2\left(a-x\right)-y\left(a-x\right)\)\(=\left(a-x\right)\left(a^2-x\right)\)

c,\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)\(=x^2y+xy^2+y^2z+yz^2+x^2z+xz^2+2xyz\)=\(x^2\left(y+z\right)+xy\left(y+z\right)+yz\left(y+z\right)+xz\left(y+z\right)\)=\(\left(y+z\right)\left(x^2+xy+yz+xz\right)\)

=\(\left(y+z\right)\left(x+y\right)\left(x+z\right)\)

Answer 5

a) \(5x-5y+ax-ay\)

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

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

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

b) \(a^3-a^2x-ay+xy\)

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

\(=a^2\left(a-x\right)-y\left(a-x\right)\)

\(=\left(a-x\right)\left(a^2-y\right)\)

c) \(xy\left(x+y\right)+yz\left(x+z\right)+xz\left(x+z\right)+2xyz\)

\(=xy\left(x+y\right)+yz\left(y+z\right)+xyz+xz\left(x+z\right)+xyz\)

\(=xy\left(x+y\right)+yz\left(x+y+z\right)+xz\left(x+y+z\right)\)

\(=xy\left(x+y\right)+z\left(x+y+z\right)\left(x+y\right)\)

\(=\left(x+y\right)\left(xy+zx+zy+z^2\right)\)

\(=\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)

\(=\left(x+y\right)\left(y+z\right)\left(z+x\right)\)

Answer 6

5x-5y+ax-ay

(5+a)x-(5+a)y

=(5+a).(x-y)