Question

Phân tích các đa thức thành nhân tử :

a) x^4+64

b) 5x^2+6xy+y^2

c) (x+y)^2+3(x+y)+2

d) x^4+2x^3-4x-4

e) x^2-7xy+10y^2

f) x^3-6x^2+12x-8

g) (a+b)^2-m^2+a+b-m

Giúp mình với mai nộp rồi MƠN NHIỀU !

Answer 1

a) \(x^4+64=x^4+4^4=\left(x^2\right)^2+\left(4^2\right)^2=\left(x^2+4^2\right)\cdot\left(x^2-4^2\right)=\left(x^2+16\right)\cdot\left(x^2-16\right)\)b)\(5x^2+6xy+y^2=5x^2+5xy+xy+y^2=5x\cdot\left(x+y\right)+y\left(x+y\right)=\left(5x+y\right)\cdot\left(x+y\right)\)c)\(\left(x+y\right)^2+3\cdot\left(x+y\right)+2=\left(x+y\right)^2+\left(x+y\right)+2\cdot\left(x+y\right)+2=\left(x+y\right)\cdot\left(x+y+1\right)+2\cdot\left(x+y+1\right)=\left(x+y+2\right)\cdot\left(x+y+1\right)\)

Answer 2

d: \(=\left(x^2-2\right)\left(x^2+2\right)+2x\left(x^2-2\right)\)

\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)

e: \(=x^2-2xy-5xy+10y^2=\left(x-2y\right)\left(x-5y\right)\)

f: \(=\left(x-2\right)^3\)

g: \(=\left(a+b+m\right)\left(a+b-m\right)+\left(a+b-m\right)\)

\(=\left(a+b-m\right)\left(a+b+m+1\right)\)