Question

Phân tích đa thức thành nhân tử

a) \(x^4-x^2y^2\)

b) \(6x^2y+3xy+9xy^2\)

c) \(4x^2-20xy+25y^2\)

d) \(x^3+6x^2+12x+8\)

e) \(64x^3+y^3\)

f) \(\dfrac{125}{216}a^3-8b^3\)

g) \(5xy-5x+10y-10\)

h) \(x^2+2xy-z^2+y^2\)

Answer 1

Lời giải:

a) \(x^4-x^2y^2=x^2(x^2-y^2)=x^2(x-y)(x+y)\)

b) \(6x^2y+3xy+9xy^2=3xy(2x+1+3y)\)

c) \(4x^2-20xy+25y^2=(2x)^2-2.2x.5y+(5y)^2\)

\(=(2x-5y)^2\)

d) \(x^3+6x^2+12x+8\)

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

Answer 2

e) \(64x^3+y^3=(4x)^3+y^3\)

\(=(4x+y)(16x^2-4xy+y^2)\)

f) \(\frac{125}{216}a^3-8b^3=(\frac{5}{6}a)^3-(2b)^3\)

\(=(\frac{5}{6}a-2b)[(\frac{5}{6}a)^2+\frac{5}{6}a.2b+(2b)^2]\)

\(=(\frac{5}{6}a-2b)(\frac{25a^2}{36}+\frac{5}{3}ab+4b^2)\)

g) \(5xy-5x+10y-10\)

\(=5x(y-1)+10(y-1)\)

\(=(5x+10)(y-1)=5(x+2)(y-1)\)

h) \(x^2+2xy-z^2+y^2\)

\(=(x^2+2xy+y^2)-z^2=(x+y)^2-z^2\)

\(=(x+y-z)(x+y+z)\)