a Đề sai: )

b

\(a^3-a^2x-ay+xy\\ =a^2\left(a-x\right)-y\left(a-x\right)\\ =\left(a-x\right)\left(a^2-y\right)\)

c

\(4x^2-y^2+4x+1\\ =\left(2x\right)^2+2.2x.1+1-y^2\\ =\left(2x+1\right)^2-y^2\\ =\left(2x+1-y\right)\left(2x+1+y\right)\)

d

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

e

\(5x^2-10xy+5y^2-5z^2\\ =5\left(x^2-2xy+y^2-z^2\right)\\ =5\left[\left(x-y\right)^2-z^2\right]\\ =5\left(x-y-z\right)\left(x-y+z\right)\)

c: =(2x+1)^2-y^2

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

d: =x^2(x^2+2x+1)

=x^2(x+1)^2

e: =5(x^2-2xy+y^2-z^2)

=5[(x-y)^2-z^2]

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

\(10x^2+10xy+5x+5y\)

\(=\left(10x^2+10xy\right)+\left(5x+5y\right)\)

\(=10x\left(x+y\right)+5\left(x+y\right)\)

\(=\left(10x+5\right)\left(x+y\right)\)

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

chỗ nào k hiểu hỏi mình lại ớ 

\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)

\(=xy\left(x+y\right)+xyz+xz\left(x+z\right)+xyz+yz\left(y+z\right)\)

\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(y+z\right)\)

\(=x\left(y+z\right)\left(x+y+z\right)+yz\left(y+z\right)\)

\(=x\left(y+z\right)\left(x+y+z+yz\right)\)

\(a,=5\left(x-y\right)+a\left(x-y\right)=\left(5+a\right)\left(x-y\right)\\ b,=a\left(x+y\right)+b\left(x+y\right)=\left(a+b\right)\left(x+y\right)\\ c,=x\left(x+1\right)+a\left(x+1\right)=\left(x+a\right)\left(x+1\right)\\ d,Sửa:x^2y+xy^2-3x-3y=xy\left(x+y\right)-3\left(x+y\right)=\left(xy-3\right)\left(x+y\right)\\ e,=xy\left(x+1\right)-\left(x+1\right)=\left(xy-1\right)\left(x+1\right)\\ f,=x^2-4=\left(x-2\right)\left(x+2\right)\\ g,=\left(x+3\right)^2-y^2=\left(x-y+3\right)\left(x+y+3\right)\\ h,=\left(x+5\right)^2-y^2=\left(x-y+5\right)\left(x+y+5\right)\\ i,=\left(x-4\right)^2-24y^2=\left(x-2\sqrt{6}y-4\right)\left(x+2\sqrt{6}y+4\right)\)

x^2-x-y^2-y

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

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

b,=(x-y)^2-z^2

=(x-y-z)(x-y+z)

Các câu còn lại lm tương tự.....

h.trang à

\(x^2-x-y^2-y\)

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

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

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

\(=\left(x-y\right)^2-z^2\)

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

\(5x+5y+ax-ay\)

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

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

\(a,=x\left(x-2\right)\\ b,=2b\left(x-3y\right)+a\left(x-3y\right)=\left(a+2b\right)\left(x-3y\right)\\ c,=x\left(x^2+2xy+y^2-4\right)=x\left[\left(x+y\right)^2-4\right]=x\left(x+y+2\right)\left(x+y-2\right)\\ d,=4-\left(x+y\right)^2=\left(2-x-y\right)\left(2+x+y\right)\\ đ,=5\left(x-y\right)\left(x+y\right)+3\left(x+y\right)^2=\left(x+y\right)\left(5x-5y+3x+3y\right)\\ =\left(x+y\right)\left(8x-2y\right)=2\left(4x-y\right)\left(x+y\right)\\ e,=3x\left(2xy-3\right)\\ b,=x\left(4x^2-4xy+y^2-4\right)=x\left[\left(2x-y\right)^2-4\right]=x\left(2x-y-2\right)\left(2x-y+2\right)\\ f,=\left(x+y\right)^2-z^2=\left(x+y-z\right)\left(x+y+z\right)\)

a,=x(x−2)b,=2b(x−3y)+a(x−3y)=(a+2b)(x−3y)c,=x(x2+2xy+y2−4)=x[(x+y)2−4]=x(x+y+2)(x+y−2)d,=4−(x+y)2=(2−x−y)(2+x+y)đ,=5(x−y)(x+y)+3(x+y)2=(x+y)(5x−5y+3x+3y)=(x+y)(8x−2y)=2(4x−y)(x+y)e,=3x(2xy−3)b,=x(4x2−4xy+y2−4)=x[(2x−y)2−4]=x(2x−y−2)(2x−y+2)f,=(x+y)2−z2=(x+y−z)(x+y+z)

A = xy + y - 2x - 2

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

= ( x + 1 )( y - 2 )

B = x² - 3x + xy - 3y

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

= ( x - 3 )( x + y )

C = 3x² - 3xy - 5x + 5y

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

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

D = xy + 1 + x + y

= y( x + 1 ) + ( x + 1 )

= ( x + 1 )( y + 1 )

E = ax - bx + ab - x²

= ( ax - x² ) + ( ab - bx )

= x( a - x ) + b( a - x )

= ( a - x )( x + b )

F = x² + ab + ax + bx

= ( ax + x² ) + ( ab + bx )

= x( a + x ) + b( a + x )

= ( a + x )( x + b )

G = a³ - a²x - ay + xy

= a²( a - x ) - y( a - x )

= ( a - x )( a² - y )

Bonus : = ( a - x )[ a² - ( √y )² ]

             = ( a - x )( a - √y )( a + √y )

H = 2xy + 3z + 6y + xz

= ( 6y + 2xy ) + ( 3z + xz )

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

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

A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1

B = x² - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)

C = 3x² - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)

D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)

E = ax - bx + ab - x² = ax - x² + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)

F = x² + ab + ax + bx = ab + ax + bx + x² = a(b + x) + x(b + x) = (a + x)(b + x)

G = a³ - a²x - ay + xy = a²(a - x) - y(a - x) = (a² - y)(a - x)

H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)

🍀Trần Nhật Quỳnh🍀 y không dương nên không thể cho vào căn nhé 

a) 

5x-5y+ax-ay = 5(x-y) +a(x-y) = (x-y)(5+a)

b) a^3 -a^2x-ay+xy = a^2(a-x) -y(a-x) = (a-x)(a^2-y)

c) xy(x+y) +yz(y+z) +xz(x+z) +2xyz = x^2.y+xy^2 +y^2.z+xz^2 +x^2.z+xz^2 +2xyz

= (x^2.y+x^2.z)+(xy^2+xz^2+2xyz)+(y^2.z+yz^2) = x^2(y+z) +x.(y+z)^2 +yz(y+z)

=(y+z)(x^2+x+yz)

a) \(A=5\left(x-y\right)+ax-ay=\left(a+5\right)\left(x-y\right)\)

b) \(B=a\left(x+y\right)-4x-4y=\left(x+y\right)\left(a-4\right)\)

c) \(C=xz+yz-5\left(x+y\right)=\left(x+y\right)\left(z-5\right)\)

d) \(D=a\left(x-y\right)+bx-by=\left(a+b\right)\left(x-y\right)\)

e) \(E=x\left(x+y\right)-5x-5y=\left(x-5\right)\left(x+y\right)\)

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

g) \(G=x^2-xy+x-y=x\left(x-y\right)+x-y=\left(x+1\right)\left(x-y\right)\)

A = 5(x - y) + ax - ay = 5(x - y) + a(x - y) = (a + 5)(x - y)

B = a(x + y) - 4x - 4y = a(x + y) - 4(x + y) = (a - 4)(x + y)

C = xz + yz - 5(x + y) = z(x + y) - 5(x + y) = (z - 5)(x + y)

D = a(x - y) + bx - by = a(x - y) + b(x - y) = (a + b)(x - y)

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

F = x² - x - y² - y = (x² - y²) - (x + y) = (x² - xy + xy - y²) - (x + y) = [x(x - y) + y(x - y)] - (x + y) = (x - y)(x + y) - (x + y) = (x + y)(x - y - 1)

G = x² - xy + x - y = x(x - y) + (x - y) = (x + 1)(x - y)                                                 

A = 5( x - y ) + ax - ay

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

= ( x - y )( 5 + a )

B = a( x + y ) - 4x - 4y

= a( x + y ) - 4( x + y )

= ( x + y )( a - 4 )

C = xz + yz - 5( x + y )

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

= ( x + y )( z - 5 )

D = a( x - y ) + bx - by

= a( x - y ) + b( x - y )

= ( x - y )( a + b )

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

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

= ( x + y )( x - 5 )

F = x² - x - y² - y

= ( x² - y² ) - ( x + y )

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

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

G = x² - xy + x - y

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

= ( x - y )( x + 1 )