Question

phân tích đa thức thành nhân tử:

a/ \(5x^2y^3-25x^3y^4+10x^3y^3\)

b/ 4x^2+12x+9

c/ 11x+11y-x^2-xy

d/ 27x^2(y-1)-9x^3(1-y)

Answer 1

a) \(5x^2y^3-25x^3y^4+10x^3y^3\)

\(=5x^2y^3\left(1-5xy+2x\right)\)

b) \(4x^2+12x+9\)

\(=\left(2x\right)^2+2.2x.3+3^2\)

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

c) \(11x+11y-x^2-xy\)

\(=11\left(x+y\right)-x\left(x+y\right)\)

\(=\left(x+y\right)\left(11-x\right)\)

d) \(27x^2\left(y-1\right)-9x^3\left(1-y\right)\)

\(=27x^2\left(y-1\right)+9x^3\left(y-1\right)\)

\(=\left(y-1\right)\left(27x^2+9x^3\right)\)

\(=9x^2\left(y-1\right)\left(3+x\right)\)

Answer 2

c/

\(11x+11y-x^2-xy\)

\(=\left(11x-x^2\right)+\left(11y-xy\right)\)

\(=x\left(11-x\right)+y\left(11-x\right)\)

= \(\left(11-x\right)\left(x+y\right)\)

Answer 3

d/

\(27x^2\left(y-1\right)-9x^3\left(1-y\right)\)

\(=9.3.x^2\left(y-1\right)+9x^2.x\left(y-1\right)\)

\(=9x^2.\left(y-1\right)\left(3+x\right)\)

Answer 4

a)= 5x^2y^3( 1-5xy+2x)
b)= (2x)^2+2.2x.3+3^3 = (2x+3)^2
c)= (11x+11y) - (x^2-xy) = 11(x+y) - x(x+y) = (x+y) (11-x)
d)= 27x^2(y-1) + 9x^3(y-1) = (y-1) (27x^2+9x^3) = (y-1) {9x^2(3+x)}
Phần d không biết mình đổi dấu đúng không

Answer 5

b/

\(4x^2+12x+9\)

\(=\left(2x\right)^2+2.2.3x+3^2\)

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

Answer 6

d/ 9x².(3xy-3x-x+xy) = 9x².3x(y-1)+x(y-1) = (y-1)4x.9x² = (y-1). 36x³

Answer 7

b)(2x)^2+2.2x.3+3^3=(2x+3)^2