Question

Phân tích đa thức sau thành nhân tử : 

a) x² - 6xy + 9y² - 25z²

b) x² - 2x - 4y² + 1

c) x² - 5x - 6

d) x² + 3x - 18

e) x² - 7x + 6

f) 3x² - 7x + 2

g) x⁴ + 64

Answer 1

a) \(x^2-6xy+9y^2-25z^2\)  
\(=\left(x^2-6xy+9y^2\right)-\left(5z\right)^2\)
\(=\left(x-3y\right)^2-\left(5z\right)^2\)
\(=\left(x-3y+5z\right)\left(x-3y-5z\right)\) 
b) \(x^2-2x-4y^2+1\) 
\(=\left(x^2-2x+1\right)-4y^2\) 
\(=\left(x-1\right)^2-\left(2y\right)^2\) 
\(=\left(x-1+2y\right)\left(x-1-2y\right)\) 
c) \(x^2-5x-6\) 
\(=x^2+x-6x+6\) 
\(=x\left(x+1\right)-6\left(x+1\right)\) 
\(=\left(x+1\right)\left(x-6\right)\) 
d) \(x^2+3x-18\) 
\(=x^2+6x-3x-18\) 
\(=x\left(x+6\right)-3\left(x+6\right)\) 
\(=\left(x+6\right)\left(x-3\right)\) 
e) \(x^2-7x+6\) 
\(=x^2-x-6x+6\) 
\(=x\left(x-1\right)-6\left(x-1\right)\) 
\(=\left(x-1\right)\left(x-6\right)\) 
f) \(3x^2-7x+2\) 
\(=\left(3x^2-6x\right)-\left(x-2\right)\) 
\(=3x\left(x-2\right)-\left(x-2\right)\) 
\(=\left(3x-1\right)\left(x-2\right)\)
g) \(x^4+64\) 
\(=\left(x^2\right)^2-8^2\) 
\(=\left(x^2\right)^2+8^2+2 . x^2 . 8-16x^2\) 
\(=\left(x^2+8\right)^2-\left(4x\right)^2\) 
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)

Answer 2

a: \(=\left(x-3y\right)^2-25z^2=\left(x-3y-5z\right)\left(x-3y+5z\right)\)

b: \(=\left(x-1\right)^2-4y^2=\left(x-1-2y\right)\left(x-1+2y\right)\)

c: \(=\left(x-6\right)\left(x+1\right)\)

d: \(=\left(x+6\right)\left(x-3\right)\)

e: \(=\left(x-1\right)\left(x-6\right)\)

f: \(=3x^2-6x-x+2=\left(x-2\right)\left(3x-1\right)\)