Question

Phân tích đa thức thành nhân tử:

a) 5a³ - 10a²b + 5ab² - 10a + 10b

b) 3x³ + 6x²y + 3xy² - 12xz²

c) x³ + 4xy² - 3x² - 6xy + 4x²y

d) 12x³ - 12x²y + 3xy² - 27xz²

Answer 1

\(a.5a^3-10a^2b+5ab^2-10a+10b=5a\left(a^2-2ab+b^2\right)-10\left(a-b\right)=5a\left(a-b\right)^2-10\left(a-b\right)=5\left(a-b\right)\left(a^2-ab-2\right)\)

\(b.3x^3+6x^2y+3xy^2-12xz^2=3x\left(x^2+2xy+y^2-4z^2\right)=3x\left[\left(x+y\right)^2-4z^2\right]=3x\left(x+y+2z\right)\left(x+y-2z\right)\)

\(c.x^3+4xy^2-3x^2-6xy+4x^2y=x\left(x^2+4y^2-3x-6y+4xy\right)=4\left[\left(x+2y\right)^2-3\left(x+2y\right)\right]=4\left(x+2y\right)\left(x+2y-3\right)\)

\(d.12x^3-12x^2y+3xy^2-27xz^2=3x\left(4x^2-4xy+y^2-9z^2\right)=3x\left[\left(2x-y\right)^2-9z^2\right]=3x\left(2x-y-3z\right)\left(2x-y+3z\right)\)