bài 1 : rút gọn biểu thức:
a) 3 (x-y)2 - 2 (x+y)2 - (x-y) (x+y)
b) 2 (2x+5)2 - 3 (4x+1) (1- 4x)
bài 2 : phân tích các đa thức sau thành nhân tử :
a) x2 - 9 + (x-3)2
b)x3 - 4x2 + 4x - xy2
c) x3 - 4x2 + 12x - 27
d) 3x2 - 7x- 10
e) 5x3 - 5x2y - 10x2 + 10xy
f) 3x2 - 6xy + 3y2 - 12z2
bài 3 :tìm x biết
a)x (4x2 - 1 ) = 0
b) 3 (x-1)2 - 3x (x-5) - 2 =0
c)x3 - x2 - x + 1 = 0
d) 2x2 - 5x - 7 =0
Bài 1 :
a ) \(3\left(x-y\right)^2-2\left(x+y\right)^2-\left(x-y\right)\left(x+y\right)\)
\(=3\left(x^2-2xy+y^2\right)-2\left(x^2+2xy+y^2\right)-\left(x^2-y^2\right)\)
\(=3x^2-6xy+3y^2-2x^2-4xy-2y^2-x^2+y^2\)
\(\)\(=2y^2-10xy\)
Câu b tương tự
Bài 2 :
a ) \(x^2-9+\left(x-3\right)^2\)
\(=\left(x-3\right)\left(x+3\right)+\left(x-3\right)^2\)
\(=\left(x-3\right)\left(x+3+x-3\right)\)
\(=2x\left(x-3\right)\)
b ) \(x^3-4x^2+4x-xy^2\)
\(=x\left(x^2-4x+4-y^2\right)\)
\(=x\left[\left(x-2\right)^2-y^2\right]\)
\(=x\left(x-2-y\right)\left(x-2+y\right)\)
c ) \(x^3-4x^2+12x-27\)
\(=x^3-9x^2+5x^2+27x-15x-3^3\)
\(=\left(x^3-9x^2+27x-3^3\right)+\left(5x-15x\right)\)
\(=\left(x-3\right)^3+5\left(x-3\right)\)
\(=\left(x-3\right)\left[\left(x-3\right)^2+5\right]\)
\(=\left(x-3\right)\left(x^2-6x+14\right)\)
d ) \(3x^2-7x-10\)
\(=3x^2+3x-10x-10\)
\(3x\left(x+1\right)-10x\left(x+1\right)\)
\(=-7x\left(x+1\right)\)
Bài 2. a) x2 - 9 + ( x - 3)2
= x2 - 32 + ( x - 3)2
= ( x - 3)( x +3) + ( x - 3)( x - 3)
= ( x - 3)( x + 3 + x - 3)
= ( x - 3)2x
b) x3 - 4x2 + 4x - xy2
= x( x2 - 4x + 4 - y2)
= x[ ( x2 - 2.2x + 22) - y2]
= x( x - 2 -y)(x - 2 +y)
c) x3 -4x2 + 12x - 27
= x3 - 33 - 4x( x - 3)
= ( x -3)( x2+ 3x +9) - 4x( x - 3)
= ( x - 3)( x2 + 3x +9 - 4x)
= ( x -3)( x2 -x + 9)
d) 3x2 - 7x - 10
= 3x2 + 3x - 10x - 10
= 3x( x + 1) - 10( x + 1)
= ( 3x - 10)( x +1)
e) 5x3 - 5x2y - 10x2 + 10xy
= 5x2( x - 2) - 5xy( x - 2)
= ( x - 2)( 5x2 - 5xy)
= ( x - 2)5x( x - y)
f) 3x2 - 6xy + 3y2 - 12z2
= 3( x2 - 2xy + y2 - 4z2)
= 3[( x - y)2 - ( 2z)2]
= 3( x - y -2z)( x - y +2z)
