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

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

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

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

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

Hok tốt

Phân tích đa thức thành nhân tử:

a. x2+4x

b. 16x2-9

c.2x-2y+bx-by

d.x2+4x-5

e.x3+x+5x2+5

f.x2+2xy-9+y2

g. x2-3xy-10y2

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

b, \(16x^2-9=\left(4x-3\right)\left(4x+3\right)\)

c, \(2x-2y+bx-by=2\left(x-y\right)+b\left(x-y\right)\)

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

d, \(x^2+4x-5=x^2+5x-x-5\)

\(=x\left(x+5\right)-\left(x+5\right)=\left(x-1\right)\left(x+5\right)\)

e, \(x^3+x+5x^2+5=x\left(x^2+1\right)+5\left(x^2+1\right)\)

\(=\left(x+5\right)\left(x^2+1\right)\)

f, \(x^2+2xy-9+y^2\)

\(=\left(x+y\right)^2-9\)

\(=\left(x+y+3\right)\left(x+y-3\right)\)

g, \(x^2-3xy-10y^2=x^2+2xy-5xy-10y^2\)

\(=x\left(x+2y\right)-5y\left(x+2y\right)\)

\(=\left(x-5y\right)\left(x+2y\right)\)

phân tích thành nhân tử

a) x^2 + x^2y - x^2z - xyz

\(x^2+x^2y-x^2z-xyz\)

\(=x\left(x+xy-xz-yz\right)\)

1. Phân tích đa thức thành nhân tử:

a. xy+y2-x-y

b.25-x2+2xy-y2

2. Tìm x, biết:

x(x-2)+x-2=0

(2x-1)2-(x+3)2=0

\(a,xy+y^2-x-y=y\left(x+y\right)-\left(x+y\right)=\left(y-1\right)\left(x+y\right)\)\(b,25-x^2+2xy-y^2=25-\left(x-y\right)^2=\left(5-x+y\right)\left(5+x-y\right)\)Bài 2:

\(x\left(x-2\right)+\left(x-2\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)

b, \(\left(2x-1\right)^2-\left(x+3\right)^2=0\)

\(\Leftrightarrow\left(2x-1-x-3\right)\left(2x-1+x+3\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(3x+2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-4=0\\3x+2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{2}{3}\end{matrix}\right.\)