a) (x - 1)(x + l)(x - 2)(x - 4).      b) (x - 2)( x 2  + 4).

c) 2y(3 x 2   +   y 2 ).                          d) 2(x + y + z) ( a   -   b ) 2 .

a. \(x^2\left(x-3\right)^2-\left(x-3\right)^2-x^2+1\)

\(=\left(x-3\right)^2\left(x^2-1\right)-\left(x^2-1\right)\)

\(=\left[\left(x-3\right)^2-1\right]\left(x^2-1\right)\)

\(=\left(x-3+1\right)\left(x-3-1\right)\left(x+1\right)\left(x-1\right)\)

\(=\left(x-2\right)\left(x-4\right)\left(x+1\right)\left(x-1\right)\)

b. \(x^3-2x^2+4x-8\)

\(=\left(x^3+4x\right)-\left(2x^2+8\right)\)

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

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

c. \(\left(x+y\right)^3-\left(x-y\right)^3\)

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

\(=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3\)

\(=6x^2y+2y^3\)

\(=2y\left(3x^2+y^2\right)\)

d. \(2a^2\left(x+y+z\right)-4ab\left(x+y+z\right)+2b^2\left(x+y+z\right)\)

\(=\left(2a^2-4ab+2b^2\right)\left(x+y+z\right)\)

\(=2\left(a^2-2ab+b^2\right)\left(x+y+z\right)\)

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

sorry ! mk đang học lớp 6

a,Từ giả thiết ta có

(x²+y²+z²)(x+y+z)²+(xy+yz+zx)²

=(x²+y²+z²)(x²+y²+z²+2xy+2yz+2zx)+(xy+yz+zx)²

Đặt x²+y²+z²=a

xy+yz+zx=b

=>(x²+y²+z²)(x²+y²+z²+2xy+2yz+2zx)+(xy+yz+zx)²

=a(a+2b)+b²

=a²+2ab+b²

=(a+b)²

=(x²+y²+z²+xy+yz+zx)²

câu b hơi dài mình gửi sau nhé

Ta có: 2(x^4+y^4+z^4)-(x^2+y^2+z^2)^2-2(x^2+y^2+z^2)(x+y+z)^2+(x+y+z)^4

Gọi x^4+y^4+z^4=a

x^2+y^2+z^2=b

x+y+z=c

=>2(x^4+y^4+z^4)-(x^2+y^2+z^2)^2-2(x^2+y^2+z^2)(x+y+z)^2+(x+y+z)^4=2a-b^2-2bc^2+c^4

=2a-2b^2+b^2-2bc^2+c^4

=2(a-b^2)+(b+c^2)^2

Ta có

2(a-b²)=2[x^4+y^4+z^4-(x^2+y^2+z^2)²]

=2[x^4+y^4+z^4-x^4-y^4-z^4-2x²y²-2y²z²-2z²x²]

=2.(-2)(x²y²+y²z²+z²x²)

=-4(x²y²+y²z²+z²x²)

Lại có

(b+c^2)^2

=[(x^2+y^2+z^2)+(x+y+z)²]²

=[(x^2+y^2+z^2)-(x^2+y^2+z^2)-2(xy+yz+zx)]²

=4(xy+yz+zx)²

=>2(a-b^2)+(b+c^2)^2

=-4(x²y²+y²z²+z²x²)+4(xy+yz+zx)²

=8xyz(x+y+z)

cauu a cua bn Đen đủi .....lm sai r

\(a,49.\left(y-4\right)^2-9y^2-36y-36=49\left(y-4\right)^2-9\left(y^2+4y+4\right)\)

\(=49\left(y-4\right)^2-9\left(y+4\right)^2=\left(7y-28\right)^2-\left(3y+12\right)^2\)

\(=\left(7y-28+3y+12\right)\left(7y-28-3y-12\right)\)

\(=\left(10y-16\right)\left(4y-40\right)=8\left(5y-8\right)\left(y-10\right)\)

\(b,xyz-\left(xy+yz+xz\right)+\left(x+y+z\right)-1\)

\(=xyz-xy-yz-xz+x+y+z-1\)

\(=\left(xyz-xy\right)-\left(xz-x\right)-\left(yz-y\right)+\left(z-1\right)\)

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

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

\(=\left(z-1\right)\text{[}x\left(y-1\right)-\left(y-1\right)\text{]}\)

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

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

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

b)x^2-(a+b)x+ab=[x^2-(a+b)x]+a

=x​(x-a-b)+a

b)x(y+z)²+y(z+x)²+z(x+y)²-4xyz

=[x(y+z)²-2xyz]+[y(z+x)²-2xyz]+z(x+y)²

=x(y²+2yz+z²-2yz)+y(x²+z²+2xz-2xz)+z(x+y)²

=x(y²+z²)+y(x²+z²)+z(x+y)²

=xy²+xz²+x²y+yz²+(xz+yz)(x+y)

=xy(x+y)+z²(x+y)+(xz+yz)(x+y)

=(x+y)(xy+z²+xz+yz)

=(x+y)[x(y+z)+z(y+z)]

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

a)x(y²-z²)+y(z²-x²)+z(x²-y²)

=x(y-z)(y+z)+yz²-x²y+x²z-y²z

=(y-z)(xy+xz)-x²(y-z)-yz(y-z)

=(y-z)(xy+xz-x²-yz)

=(y-z)[x(y-x)-z(y-x)]

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

Test

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

\(=xy^2-xz^2+yz^2-x^2y+zx^2-zy^2\)

\(=xy^2-xz^2+yz^2-x^2y+zx^2-zy^2-xyz+xyz\)

\(=\left(yz^2-xz^2-xyz+x^2z\right)-\left(zy^2-xyz-xy^2+x^2y\right)\)

\(=z\left(yz-xz-xy+x^2\right)-y\left(zy-xz-xy+x^2\right)\)

\(=\left(z-y\right)\left(yz-xz-xy+x^2\right)\)

\(=\left(z-y\right)\left[y\left(z-x\right)-x\left(z-x\right)\right]\)

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

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

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

=(x-y).2a

a x+ 2a(x-y)-y

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

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

b x^2-(a+b)x+ab

=x^2-(xa+xb)+ab

=x^2-xa-xb+ab

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

=(x-a)(x-b)

f x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)

=xy^2-xz^2+yz^2-yx^2+zx^2-zy^2

=-xzy^2-xyz^2-zyx^2

=-xyz(y+z+x)