Question

Câu 9 (1,5 điểm). Phân tích các đa thức sau thành nhân tử:

a) $5\left( x+2y \right)-15x\left( x+2y \right)$.

b) $4{{x}^{2}}-12x+9$.

c) ${{(3x-2)}^{3}}-3\left( x-4 \right)\left( x+4 \right)+{{(x-3)}^{3}}-\left( x+1 \right)\left( {{x}^{2}}-x+1 \right)$.

Answer 1

a) \(5\left(x+2y\right)-15x\left(x+2y\right)=\left(x+2y\right)\left(5-15x\right)\\ =5\left(x+2y\right)\left(1-3x\right)\)

b) \(4x^2-12x+9=\left(2x\right)^2-2.2x.3+3^2\\=\left(2x-3\right)^2\)

c) \(\left(3x-2\right)^3-3\left(x-4\right)\left(x+4\right)+\left(x-3\right)^3-\left(x+1\right)\left(x^2-x+1\right)\\ =27x^3-54x^2+18x-8-3\left(x^2-16\right)+x^3-9x^2+27x-27-\left(x^3+1\right)\\=27x^3-54x^2+18x-8-3x^2+48+x^3-9x^2+27x-27-x^3-1\\ =27x^3-57x^2+36x+12\\ =3\left(3x^3-19x^2+12x+4\right)\)

Answer 2

c) \(27x^3-54x^2+36x-8-3x^2+48+x^3-9x^2+27x-27-x^3-1\\ =27x^3-66x^2+63x+12\\=3\left(9x^3-22x^2+21x+4\right)\)

Answer 3

a, 5( x + 2y )-15x(x + 2y ).

= ( x + 2y ).( 5 -15x )

b, 4x² - 12x + 9 

= ( 2x - 3 )²

 

Answer 4

q

Answer 5

a) 5 (x + 2y) - 15x ( x + 2y )

= ( x + 2y ) (5 - 15x)

= 5 ( x + 2y ) ( 1 - 3x )

b) 4x\(^2\) - 12x + 9

= \([(\) 2x\(^2\)) - 2.2.3x + 3\(^2\)\(]\)

= ( 2x - 3 ) \(^2\)

 

Answer 6

a) (x+2y)(5-15x)
 

Answer 7

 

        a, (5-15x).(x+2y)

b,  4x

Answer 8

a) =(x+2y)(5-15x)

b) =(2x)² - 12x +3² = (2x-3)²²

c) 

Answer 9

Câu 9.

a)\(5\left(x+2y\right)\) \(-15x\left(x+2y\right)\) \(=\left(5-15x\right)\left(x+2y\right)\)\(=5\left(1-3x\right)\left(x+2y\right)\)

b) \(4x^2\)\(-12x+9\)\(=\left(2x\right)^2-12x+3^2\)\(=\left(2x+3\right)^{^{ }2}\)

c) \(\left(3x-2\right)^3-3\left(x-4\right)\left(x+4\right)+\left(x-3\right)^3-\left(x+1\right)\left(x^2-x+1\right)\)

= \(27x^3-54x^2+36x-8-3x^2+48+x^3-9x^2+27x-27-x^3-1\)

= \(27x^3-66x^2+63x+12\)

Answer 10

a) (X+2y).(5-15x)

b)x(4x-3) +9

Answer 11

Kobt

Answer 12

a, \(5\left(x+2y\right)-15x\left(x+2y\right)\) = \(\left(5-15x\right)\left(x+2y\right)\)

b, \(4x^2-12+9\) = \(2x^2-2.2.3+3^2\) = \(\left(2x+3\right)^2\)