Question

PTĐTTNT

a/ 3x^3 - 4x^2 + x

b/ ax^2 + by^2 - ay^2 - bx^2

c/ 3x^2 - 6xy - 12 + 3y^2

d/ 12x. ( 3 - 4x ) - 21 + 28x

Answer 1

a.

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

\(=x\left[3x\left(x-1\right)-\left(x-1\right)\right]=x\left(x-1\right)\left(3x-1\right)\)

b.

\(ax^2+by^2-ay^2-bx^2=a\left(x^2-y^2\right)-b\left(x^2-y^2\right)\)

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

c.

\(3x^2-6xy-12+3y^2=3\left(x^2-2xy+y^2-4\right)\)

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

d.

\(12x\left(3-4x\right)-21+28x=12x\left(3-4x\right)-7\left(3-4x\right)\)

\(=\left(3-4x\right)\left(12x-7\right)\)