Question

Phân tích đa thức sau thành nhân tử

e) 3x( x - 1 )² - ( 1 - x )³

f) 9x⁴ - \(\frac{1}{4}\)

g) a - ( a - b )²

h) ( x - y )² - ( m + n )² 

i) 9( a - b)² - 4 ( x - y )²

Answer 1

f, 9x⁴-\(\frac{1}{4}\)= (3x²)²-\(\left(\frac{1}{2}\right)^2\)= (3x²-\(\frac{1}{2}\))(3x²+\(\frac{1}{2}\))

h, (x-y)²-(m+n)²=(x-y+m+n)(x-y-m-n)

i, 9(a-b)²-4(x-y)²= (3a-3b)²-(2x-2y)²=(3a-3b+2x-2y)(3a-3b-2x+2y)

Answer 2

x^4 - 2x^3 - 2x^2 - 2x - 3 
= ( x^4 - 3x^3 ) + ( x^3 - 3x^2 )+ ( x^2 - 3x ) + ( x - 3) 
= x^3 ( x - 3 ) + x^2 ( x - 3 ) + x ( x - 3 ) + ( x - 3 ) 
= ( x - 3 ) ( x^3 + x^2 + x + 1 ) 
= ( x - 3 ) [( x^3 + x^2 ) + ( x + 1 )] 
= ( x - 3 ) [ x^2 ( x + 1 ) + ( x + 1)] 
= ( x - 3 ) ( x + 1 ) ( x^2 + 1 )