Question

Phân tích đa thức thành nhân tử

a) x² + 4x – y² + y

b) 3x² + 6xy+ 3y²- 3z²

c) X² – 2xy + y² – z² + 2zt – t²

d) 2x² + 4x – 2 - 2y²

e) 2xy – x² – y² + 16

f) 2x – 2y – x² + 2xy – y²

g) x⁴ + 4

h) x³ + 2x² + 2x +1

Answer 1

b, \(3x^2+6xy+3y^2-3z^2=3\left(x^2+2xy+y^2\right)-3z^2\)

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

c,\(=\left(x^2-2xy+y^2\right)-\left(z^2-2zt+t^2\right)=\left(x-y\right)^2-\left(z-t\right)^2\)

\(=\left(x-y+z-t\right)\left(x-y-z+t\right)\)

e,\(=-\left(x^2-2xy+y^2-16\right)=-\left[\left(x-y\right)^2-16\right]\)

\(=-\left(x-y-4\right)\left(x-y+4\right)\)

f, \(=2\left(x-y\right)-\left(x^2-2xy+y^2\right)=2\left(x-y\right)-\left(x-y\right)^2\)

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

g,\(=x^4+4x^2+4-4x^2=\left(x^2+2\right)^2-\left(2x\right)^2\)

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

h,\(=x^3+x^2+x^2+x+x+1=x^2\left(x+1\right)+x\left(x+1\right)+\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2+x+1\right)\)

Answer 2

câu đề là a) x² + 4x – y² + 4 nha

Answer 3

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

Answer 4

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

Answer 5

mấy bài còn lại cứ tương tự như vậy nha