Question

Phân tích đa thức thành nhân tử:

a.\(3x^2-12y^2\)

b.\(5xy^2-10xyz+5xz^2\)

c.\(x^3+3x^2+3x+1-27z^3\)

d.\(x^2-2xy+y^2-xz+y^2\)

e.\(x^2-y^2-x+9\)

g.\(\left(a+b+c\right)^3-a^3-b^3-c^3\)

h.\(a^3+b^3+c^3-3abc\)

Answer 1

a.3x^{2 -} 12y² = 3(x²-4y²)
=3[x²-(2y)² ]
=3.(x-2y).(x+2y)
b.5xy²-10xyz + 5xz²
=5x.(y^2 - 2yz + z^2)
=5x.(y-z)^2

d.x^2 - 2xy +y^2-xz + y^2
= (x^2 - 2xy +y^2 ) - (xz-y^2)
= (x-y)^2 - (xz - y^2)
e.x^2 - y^2 -x +9
= (x^2 - x ) - (y^2 - 9 )
= x(x-1) - (y-3)(y+3)

Answer 2

g: \(=a^3+b^3+c^3-a^3-b^3-c^3+3\left(a+b\right)\left(b+c\right)\left(a+c\right)\)

\(=3\left(a+b\right)\left(b+c\right)\left(a+c\right)\)

h: \(=\left(a+b\right)^3+c^3-3ab\left(a+b\right)-3abc\)

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

\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-ac-bc\right)\)

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

b:\(=5x\left(y^2-2yz+z^2\right)=5x\left(y-z\right)^2\)