Question

Phân tích các đa thức sau thành nhân tử

a) \(x^2-xy+x-y\)

b) \(xz+yz-5\left(x+y\right)\)

c) \(3x^2-3xy-5x+5y\)

Answer 1

Bài giải:

a) x² – xy + x – y = (x² – xy) + (x - y)

= x(x - y) + (x -y)

= (x - y)(x + 1)

b) xz + yz – 5(x + y) = z(x + y) - 5(x + y)

= (x + y)(z - 5)

c) 3x² – 3xy – 5x + 5y = (3x² – 3xy) - (5x - 5y)

= 3x(x - y) -5(x - y) = (x - y)(3x - 5).

Answer 2

\(a) x^2 - xy+x-y\) \(= (x^2 - xy) + ( x- y) \)

\(=x(x-y) + (x-y)\)

\(= (x-y) (x+1)\)

\(b) xz + yz - 5(x+y)\) \(= (xz + yz) - 5(x+y)\)

\(= z(x+y) - 5(x+y)\)

\(= (x+y) (z-5)\)

\(c) 3x^2 - 3xy - 5x +5y = (3x^2-3xy) - (5x-5y)\)

\(= 3x(x-y) - 5(x-y)\)

\(= (x-y)(3x-5)\)

Answer 3

a) x² - xy + x - y = x (x - y) + (x - y)

=(x - y) (x + 1)

b) xz + yz - 5 (x + y) = z (x + y) - 5 (x + y)

=(x + y) (z - 5)

c) 3x² - 3xy - 5x + 5y = 3x (x - y) - 5 (x - y)

= (x - y) (3x - 5)

Answer 4

a, \(x^2-xy+x-y=\left(x^2+x\right)-\left(\text{ x }y-y\right)\)

=\(\left(\text{ x }^2+\text{ x }\right)-\left(\text{ x }y+y\right)\)

=$x$\(\left(\text{x}+1\right)-y\left(\text{x}+1\right)\)

=\(\left(x-y\right)\left(\text{x}+1\right)\)

b, $xz+yz-5\left(x+y\right)$

=xz + yz - 5x - 5 y

=\(\left(\text{x }z-5\text{x }\right)+\left(yz-5y\right)\)

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

=\(\left(\text{x}+y\right)\left(z-5\right)\)

c, \(3\text{x}^2-3\text{x}y-5\text{x}+5y=\left(3\text{x}^2-3\text{x}y\right)-\left(5\text{x}+5y\right)\)

=\(\left(3\text{x}^2-3\text{x}y\right)-\left(5\text{x}-5y\right)\)

=3x\(\left(\text{x}-y\right)-5\left(\text{x}-y\right)\)

=\(\left(3\text{x}-5\right)\left(\text{x}-y\right)\)