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a) x2 - 9 + (x - 3)
= (x- 3)(x + 3) + (x - 3)
= (x - 3)(x + 3 + 1)
= (x - 3)(x + 4)
b) x3 - 4x2 + 4x - xy2
= x(x2 - 4x + 4 - y2)
= \(x\left [ (x - 2)^{2} - y^{2}\right ]\)
= x(x - 2 - y)(x - 2 + y)
= x(x - y - 2)(x + y - 2)
c) x3 - 4x2 + 12x - 27
= x3 - 27 - 4x2 + 12x
= (x - 3)(x2 + 3x + 9) - 4x(x - 3)
= (x - 3)(x2 + 3x + 9 - 4x)
= (x - 3)(x2 - x + 9)
e) 5x3 - 5x2y - 10x2 + 10xy
= 5x(x2 - xy - 2x + 2y)
= \(5x\left [ x(x - y) - 2(x - y) \right ]\)
= 5x(x - y)(x - 2)
câu f pn coi lại mũ của 3x nha nếu mũ 2 thì lm như dưới
f) 3x2 - 6xy + 3y2 - 12z2
= 3(x2 - 2xy + y2 - 4z2)
= \(3\left [ (x - y)^{2} - (2z)^{2} \right ]\)
= 3(x - y - 2z)(x - y + 2z)
pn coi lại đề câu d với f nhé
a) x3 - 4x2 + 4x - xy2
= x( x2 - 2.2x + 22 - y2)
= x[( x- 2)2 - y2]
= x( x -2 -y).(x - 2 +y)
b) 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)
c) 5x3 - 5x2y - 10x2 + 10xy
= 5x( x2 - xy - 2x + 2y)
= 5x[ x( x -y) - 2( x -y)]
= 5x.( x -2).( x -y)
d) 3x2 - 6xy + 3y2 - 12z2
= 3( x2 - 2xy + y2 - 4z2)
= 3.[ ( x -y)2 - ( 2z)2]
= 3.( x - y - 2z ).( x -y +2z)
a) 3x2 - 7x + 2
= 3x2 - 6x - x + 2
= (3x2 - 6x) - (x - 2)
= 3x (x - 2) - (x - 2)
= (3x - 1) (x - 2)
a, x\(^3\)+9x\(^2\)-4x-36
=x(x\(^2\)-4)+9(x\(^2\)-4)
=(x\(^2\)-4)(x+9)
=(x-2)(x+2)(x+9)
b,x\(^2\)-7x-10
=x\(^2\)-5x-2x-10
=(x-5)(x-2)
{câu này hình như sai đê bài hay sao ý}
a) co sai de ko
b)x3-2x2+4x2-8x+3x-6=x2(x-2)+4x(x-2)+3(x-2)=(x-2)(x2+4x+3)=(x-2)(x+3)(x+1)
c)x3-2x2+2x2-4x-3x+6=x2(x-2)+2x(x-2)-3(x-2)=(x-2)(x2+2x-3)=(x-2)(x+3)(x-1)
d)x3-3x2+x2-3x-2x+6=x2(x-3)+x(x-3)-2(x-3)=(x-3)(x2+x-2)=(x-3)(x+2)(x-1)
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 ) \(3x^2-7x-10\)
\(=3x^2+3x-10x-10\)
\(3x\left(x+1\right)-10x\left(x+1\right)\)
\(=-7x\left(x+1\right)\)
a,\(x^2-9+\left(x-3\right)^2\)
\(=\left(x+3\right)\left(x-3\right)+\left(x-3\right)^2\)
\(=\left(x+3+x-3\right)\left(x-3\right)\)
\(=2x\left(x-3\right)\)
b,\(x^3-4x^2+4x-xy^2\)
\(=x\left(x^2-4x+4-y^2\right)\)
\(=x\left[(x-2)^2-y^2\right]\)
\(=x\left(x-2+y\right)\left(x-2-y\right)\)
c,\(3x^2-7x-10\)
\(=3x^2-10x+3x-10\)
\(=\left(3x^2+3x\right)+\left(-10x-10\right)\)
\(=3x\left(x+1\right)-10\left(x+1\right)\)
\(=\left(3x-10\right)\left(x+1\right)\)
d,\(5x^3-5x^2y-10x^2+10xy\)
\(=\left(5x^3-5x^2y\right)+\left(-10x^2+10xy\right)\)
\(=5x^2\left(x-y\right)-10x\left(x-y\right)\)
\(=\left(5x^2-10x\right)\left(x-y\right)\)
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