\(x^3+1-x^2-x\)

\(=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-2x+1\right)\)

\(=\left(x+1\right)\left(x-1\right)^2\)

\(x+y-x^3-y^3\)

\(=\left(x+y\right)-\left(x+y\right)\left(x^2-xy+y^2\right)\)

\(=\left(x+y\right)\left(1-x^2+xy-y^2\right)\)

a ) \(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2-4c^2\right)\)

\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)

\(=4\left(a-b-2c\right)\left(a-b+2c\right)\)

b ) \(x^2-25+y^2+2xy\)

\(=\left(x^2+2xy+y^2\right)-25\)

\(=\left(x+y\right)^2-5^2\)

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

c )

\(x^2y-x^3-9y+9x\)

\(=x^2\left(y-x\right)-9\left(y-x\right)\)

\(=\left(y-x\right)\left(x^2-9\right)\)

\(=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)

d )\(x^2\left(x-1\right)+16\left(1-x\right)\)

\(=x^2\left(x-1\right)-16\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2-16\right)\)

\(=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)

 TL:

\(4x^2-y^2+4x+1\)

\(=\left(2x-1\right)^2-y^2\)

\(=\left(2x-1+y\right)\left(2x-1-y\right)\)

\(x^3-x+y^3-y\)

\(=\left(x+y\right)\left(x^2-xy+x^2\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(x^2-xy+x^2-1\right)\)

a) (3x-1)(9x²+3x+1)=27x³-1

27x³-1=27x³-1

27x³-1-(27x³-1)=0

27x³-1-27x³+1=0

⇒x=0

b)(x²-5x+25)(x+5)=x³+125

(x+5)(x²-x.5+5²)=x³+125

x³+125-(x³+125)=0

x³+125-x³-125=0

⇒x=0

c)(x-3)(x²-6x+9)=(x-3)³

x³-3³-(x-3)³=0

x³-27-x³+27=0

⇒x=0

d) Đề phải là thế này chứ \(\left(x-y+4\right).\left(x-y-4\right)\)

\(=\left(x-y\right)^2-4^2\)

\(=\left(x-y\right)^2-16\)

\(=x^2-2.x.y+y^2-16\)

\(=x^2-2xy+y^2-16.\)

Chúc bạn học tốt!

a. 6x³y² ( 2-x) + 9x²y² (x-2)

= -6x³y² (x-2) + 9x²y² ( x-2)

= (x-2) 3x²y² ( -2x + 3)

b. x² - 4x + 4y - y² 

= x² - y² - (4x - 4y )

= (x-y)(x+y) - 4( x-y)

= (x-y)(x+y-4)

c. 81x² + 6yz -9y²-z² 

= 81x²  - (9y² - 6yz + z² )

= (9x)² - ( 3y - z )²

= (9x + 3y -z)(9x - 3y + z )

\(a,=6x^3y^2\left(2-x\right)-9x^2y^2\left(2-x\right)\)

\(=\left(2-x\right)\left(6x^3y^2-9x^2y^2\right)=\left(2-x\right)3x^2y^2\left(2x-3\right)\)

\(f,=\left(x-3-x-2\right)\left(x-3+x+2\right)\)

\(=-5\left(2x-1\right)\)

\(g,=\left(x-3\right)\left(x+3\right)+2\left(x+3\right)\)

\(=\left(x+3\right)\left(x-3+2\right)\)

\(=\left(x+3\right)\left(x-1\right)\)

a)\(81x^2-6yz-9y^2-z^2\)

\(=81x^2-\left(z-3y\right)^2\)

\(=\left(9x-z+3y\right)\left(9x+z-3y\right)\)

b)\(x^2y-x^3-9y+9x\)

\(=x^2\left(y-x\right)-9\left(y-x\right)\)

\(=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)

c)\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2-4z^2\right)\)

\(=3\left[\left(a-b\right)^2-4z^2\right]\)

\(=3\left(a-b-2z\right)\left(a-b+2z\right)\)

a)\(81x^2-6yz-9y^2-z^2=\left(9x\right)^2-\left(9y^2+6yz+z^2\right)=\left(9x\right)^2-\left(3y+z\right)^2=\left(9x-3y-z\right)\left(9x+3y+z\right)\)b)\(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x^2-9\right)\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)

c)\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)

a) \(\left(2x-y\right)\left(4x^2-2xy+y^2\right)\)

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

\(=\left(2x-y\right)^3\)

b) \(\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2\)

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

những câu khác tương tự

\(x^4-y^4\)

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

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

\(125x^3-1\)

\(=\left(5x\right)^3-1^3\)

\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)

\(a,\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)

\(b,\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2=2x^2-3xy+5y^2\)

\(c,\left(2x^3-21x^2+67x-60\right):\left(x-5\right)=\left(2x^3-10x^2-11x^2+55x+12x-60\right):x-5=\left[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\right]:\left(x-5\right)=\left(x-5\right)\left(2x^2-11x+12\right)\left(x-5\right):\left(x-5\right)=2x^2-11x+12\)