bài 1:

a) x(x-2)-5y-(x-2)=(x-5y)(x-2)

b) =(2x-3-4x)(2x-3+4x)=(-2x-3)(6x-3)

bài 2 bạn tự luyện nhé

????

a) 3a +3b -a²-ab

= 3.(a+b) -a.(a+b)=(3-a).(a+b)

b) x² +x +y²-y-2xy

=(x² - 2xy+y²) +(x-y)

=(x-y).(x-y+1)

c) -x² +7x -6

= -x² + x +6x-6

= x.(1-x) -6.(1-x) = (1-x).(x-6)

d) 5x³y -10x²y² +5xy³

= 5xy.(x² -2xy +y²) = 5xy.(x-y)²

e) 2x² +7x -15

= 2x² -3x +10x -15

=x.(2x-3) + 5.(2x-3)

=(2x-3).(x+5)

g) x² -2x +2y -xy

=x.(x-2)-y.(x-2)

=(x-y).(x-2)

h) bn go lai de ho mk dc k?

a) Xem lại đề

b) x³ - 4x²y + 4xy² - 9x

= x(x² - 4xy + 4y² - 9)

= x[(x² - 4xy + 4y² - 3²]

= x[(x - 2y)² - 3²]

= x(x - 2y - 3)(x - 2y + 3)

c) x³ - y³ + x - y

= (x³ - y³) + (x - y)

= (x - y)(x² + xy + y²) + (x - y)

= (x - y)(x² + xy + y² + 1)

d) 4x² - 4xy + 2x - y + y²

= (4x² - 4xy + y²) + (2x - y)

= (2x - y)² + (2x - y)

= (2x - y)(2x - y + 1)

e) 9x² - 3x + 2y - 4y²

= (9x² - 4y²) - (3x - 2y)

= (3x - 2y)(3x + 2y) - (3x - 2y)

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

f) 3x² - 6xy + 3y² - 5x + 5y

= (3x² - 6xy + 3y²) - (5x - 5y)

= 3(x² - 2xy + y²) - 5(x - y)

= 3(x - y)² - 5(x - y)

= (x - y)[(3(x - y) - 5]

= (x - y)(3x - 3y - 5)

a)x³-6x²+9x=x(x²-6x+9)=x(x-3)²

b)x²-2x-4y²-4y=(x²-2x+1)-(4y²+4y+1)=(x-1)²-(2y+1)²=(x-1-2y-1)(x-1+2y+1)=(x-2y-2)(x+2y)

c)x²-x+xy-y=x(x-1)+y(x-1)=(x-1)(x+y)

d)3x²-6xy-75+3y²=3[(x²-2xy+y²)-25]=3[(x-y)²-5²]=3(x-y-5)(x-y+5)

e)2x²-5x-7=(2x²+2x)-(7x+7)=2x(x+1)-7(x+1)=(x+1)(2x-7)

f)x⁴+36=x⁴+12x²+36-12x²=(x²+6)²-12x²=(x²-\(\sqrt{12}x\)+6)(x²+\(\sqrt{12}x\)+6)

h)x⁴+4y⁴=x⁴+4x²y²+4y²-4x²y²=(x²+2y²)-4x²y²=(x²+2y²-2xy)(x²+2y²+2xy)

Bài 1:

a) \(7x^2\left(x^2-5x+1\right)=7x^4-35x^3+7x^2\)

b) \(\left(2x-3\right)\left(x+7\right)=2x^2+11x-21\)

Bài 2:

a) \(4x^2y-8x^3y^2=4x^2y\left(1-2xy\right)\)

b) \(2x-4y-ax+2ay=x\left(2-a\right)-2y\left(2-a\right)=\left(2-a\right)\left(x-2y\right)\)

Trả lời:

a, 5x² + 10xy + 5y² = 5 ( x² + 2xy + y² ) = 5 ( x + y )² 

b, x² + 3x - y² + 3y = ( x² - y² ) + ( 3x + 3y ) = ( x - y )( x + y ) + 3 ( x + y ) = ( x + y )( x - y + 3 )

c, x² + 5x - y² + 5y = ( x² - y² ) + ( 5x + 5y ) = ( x - y )( x + y ) + 5 ( x + y ) = ( x + y )( x - y + 5 )

d, 3x² - 3y² - 2 ( x - y )² = 3 ( x² - y² ) - 2 ( x - y )² = 3 ( x - y )( x + y ) - 2 ( x - y )² = ( x - y )[ 3 ( x + y ) - 2 ] = ( x - y )( 3x + 3y - 2 )

e, x² - 2x - 4y² - 4y = ( x² - 4y² ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2 ( x + 2y ) = ( x + 2y )( x - 2y - 2 )

a) 5x²+10xy+5y²

=5(x²+2xy+y²)

=5(x+y)²

b) x²+3x-y²+3y

=(x²-y²)+(3x+3y)

=(x-y)(x+y)+3(x+y)

=(x+y)(x-y+3)

c) x²+5x-y²+5y

=(x²-y²)+(5x+5y)

=(x-y)(x+y)+5(x+y)

=(x+y)(x-y+5)

d) 3x²-3y²-2(x-y)²

=3(x²-y²)-2(x-y)²

=3(x-y)(x+y)-2(x-y)²

=(x-y)[3(x+y)-2(x-y)]

e) x²-2x-4y²-4y

=(x²-4y²)-(2x+4y)

=(x-2y)(x+2y)-2(x+2y)

=(x+2y)(x-2y-2)

#H

tách nhỏ câu hỏi ra bạn

\(a.10x\left(x-y\right)-6y\left(y-x\right)\\ =10x\left(x-y\right)+6y\left(x-y\right)\\ =\left(10x-6y\right)\left(x-y\right)\\ =2\left(5x-3y\right)\left(x-y\right)\)

\(b.14x^2y-21xy^2+28x^3y^2\\ =7xy\left(x-y+xy\right)\)

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

\(d.\left(x+1\right)^2-25\\ =\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)

c/\(x^2-2x=2y-xy\)

\(x^2-2x+xy-2y=0\)

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

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

d/\(x^2+4xy-16+4y^2\)

\(=\left(x^2+4xy+4y^2\right)-16\)

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

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

b/\(2x^2+7x-15\)

\(=2x^2+10x-3x-15\)

\(=\left(2x^2+10x\right)-\left(3x+15\right)\)

\(=2x\left(x+5\right)-3\left(x+5\right)\)

\(=\left(2x-3\right)\left(x+5\right)\)