Question

phân tích các đa thức sau thành nhân tử

a) 3x^2y^2 -6 x^2y^3 + 9x^2y^2

b) 5x^2y^3 - 25x^3y^4 + 10 x^3y^3

c) 12x^2y - 18xy^2 - 30y^2

d) 5 (x-y) - y (x-y)

e) y (x-z) + 7 (z-x)

f) 27x^2 (y-1) -9x^3 (1-y)

Answer 1

1, \(3x^2y^2-6x^2y^3+9x^2y^2\)

\(\Leftrightarrow12x^2y^2-6x^2y^2\)

\(\Leftrightarrow3x^2y^2\left(4+2y\right)\)

Answer 2

5x^2y^3 - 25x^3y^4 + 10x^3y^3

\(\Leftrightarrow5x^2y^3\left(1-5xy+2x\right)\)

Answer 3

\(12x^2y-18xy^2+30y^2\)

\(\Leftrightarrow6y\left(2x^2-3xy-5y\right)\)

Answer 4

5(x-y)-y(x-y)

\(\Leftrightarrow\)(5-y)(x-y)

Answer 5

y(x-z)+7(z-x)

\(\Leftrightarrow\)y(x-z)-7(x-z)

\(\Leftrightarrow\)(y-7)(x-z)

Answer 6

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

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

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

\(\Leftrightarrow9x^2\left(3x+x\right)\left(y-1\right)\)