1. phân tích đa thức thành nhân tử
a) \(a^2-ab+a-b\)
b) \(x^3-2xy-x^2y+2y^2\)
c) \(a^2-x^2+2a+1\)
d) \(m^2-a^2+2ab-b^2\)
e) \(25b^4-x^2-4x-4\)
f) \(3x^2+6xy+3y^2-3z^2\)
g) \(a^2-2ax-b^2-2by+x^2-y^2\)
2. phân tích đa thức ra thừa số
a) \(a^3-2a^2b+ab^2\)
b) \(5ax^4+10ax^3y+5ax^2y^3\)
c) \(2x^2+4x+2-2y^2\)
d) \(2xy-x^2-y^2+9\)
e) \(x^3+2x^2y+xy^2-16x\)
f) \(a^3-a^2-a+1\)
g) \(m^2+am+ay-y^2\)
h) \(3xy+y^2-3x-1\)
k) \(x^3-xy^2+x^2y-y^3\)
l) \(a^3-ma-mb+b^3\)
3. tìm x:
a) \(x\left(x-1\right)+x-1=0\)
b) \(3\left(x-3\right)-4x+12=0\)
c) \(x^3-5x=0\)
d) \(\left(3x-2\right)^2-\left(x+2\right)^2=0\)
e) \(x^2-9-4\left(x+3\right)=0\)
f) \(2\left(x+2\right)-x^2+4x-4=0\)
4. phân tích đa thức thành nhân tử
a) \(x^2-6x+7\)
b) \(y^2+y-20\)
c) \(2x^2-x-6\)
d) \(3m^2+2m-8\)
e) \(x^4+64\)
f) \(a^4+4b^4\)
Bài 3 :
a ) \(x\left(x-1\right)+x-1=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
Vậy...........
b ) \(3\left(x-3\right)-4x+12=0\)
\(\Leftrightarrow3\left(x-3\right)-4\left(x-3\right)=0\)
\(\Leftrightarrow\) \(\left(x-3\right)=0\Rightarrow x=3\)
Vậy............
Các câu sau tương tự
1.a)a2-ab+a-b=a2+a-ab-b=a(a+1)-b(a+1)=(a-b)(a+1)
b)x3-2xy-x2y+2y2=x3-x2y-2xy+2y2=x2(x-y)-2y(x-y)=(x2-2y)(x-y)
c)a2-x2+2a+1=a2+2a+1-x2=(a+1)2-x2=(a+1-x)(a+1+x)
d)m2-a2+2ab-b2=m2-(a2-2ab+b2)=m2-(a-b)2=(m-a+b)(m+a-b)
e)25b4-x2-4x-4=(5a2)2-(x2+4x+4)=(5a2)2-(x+2)2=(5a2-x-2)(5a2+x+2)
f)3x2+6xy+3y2-3z2=3(x2+2xy+y2-z2)=3((x+y)2-z2)=3(x+y-z)(x+y+z)
g)a2-2ax-b2-2by+x2-y2=a2-2ax+x2-(b2+2by+y2)=(a-x)2-(b+y)2=(a-x-b-y)(a-x+b+y)
