a,  a(x-y) + bx - by = a(x - y ) +b.(x-y) = (x-y)(a-b)

b, ac+bc + a + b = c.(a+b) +(a+b) = (a+b)(c+1)

c, \(5a^2-5ax-7a+7x=5a.\left(a-x\right)-7.\left(a-x\right)=\left(a-x\right)\left(5a-7\right)\)

d, \(7z^2-7yz-4z+4y=7z.\left(z-y\right)-4.\left(z-y\right)=\left(z-y\right)\left(7z-4\right)\)

e, \(x^3+3x^2+3x+9=x^2.\left(x+3\right)+3\left(x+3\right)=\left(x+3\right)\left(x^2+3\right)\)

g, \(pq-p^2-5\left(p-q\right)=p.\left(q-p\right)+5\left(q-p\right)=\left(q-p\right)\left(p+5\right)\)

bạn viết lại đề đi, có số mũ, xuống dòng chứ thế này ai mà giải được

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

\(=x\left(x+1\right)+2y\left(x+1\right)\)

\(=\left(x+1\right)\left(2y+x\right)\)

\(7x^2-7xy-5x+5y\)

\(=7x\left(x-y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(7x-5\right)\)

a)x²+2xy+x+2y

=(2xy+x²)+(2y+x)

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

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

b)7x²-7xy-5x+5y

=(5y-7xy)+(7x²-5x)

=y(5-7x)-x(5-7x)

=(5-7x)(y-x)

c)x²-6x+9-9y²

=(x²+3xy-3x)-(3xy+9y²-9y)-(3x+9y-9)

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

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

d)x³-3x²+3x-1+2(x²-x)

Ta thấy x=1 là nghiệm của đa thức

=>đa thức có 1 hạng tử là x-1

=(x-1)(x²+1)

e) (x+y)(y+z)(z+x)+xyz

đề sai

f)x(y²-z²)+y(z²-x²)

=(xy²+yz²)+(x²y+xz²)

=y(xy+z²)-x(xy+z²)

=(y-x)(xy+z²)

a)x²+2xy+x+2y

=(2xy+x²)+(2y+x)

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

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

b)7x²-7xy-5x+5y

=(5y-7xy)+(7x²-5x)

=y(5-7x)-x(5-7x)

=(5-7x)(y-x)

c)x²-6x+9-9y²

=(x²+3xy-3x)-(3xy+9y²-9y)-(3x+9y-9)

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

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

d)x³-3x²+3x-1+2(x²-x)

Ta thấy x=1 là nghiệm của đa thức

=>đa thức có 1 hạng tử là x-1

=(x-1)(x²+1)

e) (x+y)(y+z)(z+x)+xyz

đề sai

f)x(y²-z²)+y(z²-x²)

=(xy²+yz²)+(x²y+xz²)

=y(xy+z²)-x(xy+z²)

=(y-x)(xy+z²)

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

= x^2 - ax - bx + ab

= (x^2 - ax) - (bx - ab)

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

= (x-b)(x-a) 

b)7x^3-3xyz-21x^2+9z

= 

c)4x+4y-x^2(x+y)

= 4(x + y) - x^2(x+y)

= (4-x^2) (x+y)

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

d) y^2+y-x^2+x

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

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

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

e)4x^2-2x-y^2-y

= [(2x)^2 - y^2] - (2x +y)

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

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

f)9x^2-25y^2-6x+10y

= 

ko biết làm

Bài `1`

\(a,5x^2-10xy=5x\left(x-2y\right)\\ b,3x\left(x-y\right)-6\left(x-y\right)=\left(x-y\right)\left(3x-6\right)\\ =3\left(x-y\right)\left(x-2\right)\\ c,2x\left(x-y\right)-4y\left(y-x\right)=2x\left(x-y\right)+4y\left(x-y\right)\\ =\left(x-y\right)\left(2x+4y\right)=2\left(x-y\right)\left(x+2y\right)\\ d,9x^2-9y^2=\left(3x\right)^2-\left(3y\right)^2=\left(3x-3y\right)\left(3x+3y\right)\\ f,xy-xz-y+z=\left(xy-xz\right)-\left(y-z\right)\\ =x\left(y-z\right)-\left(y-z\right)=\left(y-z\right)\left(x-1\right)\)

Bài `3`

\(a,3x^2+8x=0\\ \Leftrightarrow x\left(3x+8\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x+8=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x=-8\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{8}{3}\end{matrix}\right.\)

\(b,9x^2-25=0\\ \Leftrightarrow\left(3x\right)^2-5^2=0\\ \Leftrightarrow\left(3x-5\right)\left(3x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x-5=0\\3x+5=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}3x=5\\3x=-5\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-\dfrac{5}{3}\end{matrix}\right.\)

\(c,x^3-16x=0\\ \Leftrightarrow x\left(x^2-16\right)=0\\ \Leftrightarrow x\left(x-4\right)\left(x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)

\(d,x^3+x=0\\ \Leftrightarrow x\left(x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2+1\in\varnothing\\x=0\end{matrix}\right.\Rightarrow x=0\)

dài quá mình làm 3 câu đầu thôi nhé!

a)7x^2-14xy

=7x(x-2y)

b) 3x^2-6xy+3y^2

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

c) x^2-4z^2-2xy+y^2

=(x^2-2xy+y^2)-4z^2

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

=3(x-y)^2

c) 

a) \(x^2-81=\left(x-9\right)\left(x+9\right)\)

b) \(4x^2-25=\left(2x-5\right)\left(2x+5\right)\)

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

d) \(x^2+6xy+9y^2=\left(x+3y\right)^2\)

e) \(6x-9-x^2=-\left(x^2-6x+9\right)=-\left(x-3\right)^2\)

f) \(x^2-4x^2+4y^2+4xy=\left(x^2+4xy+4y^2\right)-4x^2=\left(x+2y\right)^2-4x^2\\ =\left(x+2y+2x\right)\left(x+2y-2x\right)=\left(3x+2y\right)\left(2y-x\right)\)

g) \(\left(a+b\right)^3+\left(a-b\right)^3=\left(a+b+a-b\right)\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

\(=2a\left(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2\right)=2a\left(a^2+3b^2\right)\)

h) \(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\\ =\left(4x+2\right)\cdot2x=4x\left(2x+1\right)\)

Bạn tải ứng dụng PhotoMath về nha. Ứng dụng này sẽ giải toán số chi tiết

a) \(x^3-4x^2-12x+27\)

\(=\left(x^3+27\right)-\left(4x^2+12x\right)\)

\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)

\(=\left(x+3\right)\left(x^2-7x+9\right)\)

b) \(x^3-3x^2-4x+12\)

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

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

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

a) \(9x^2+6xy+y^2=\left(3x+y\right)^2\)

b) \(6x-9-x^2=-\left(x-3\right)^2\)

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

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

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

\(=2x.\left(-2y\right)=-4xy\)

e) \(\left(2x-1\right)^2-\left(x-1\right)^2\)

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

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

g) \(x^2+5x-6\)

\(=x^2+6x-x-6\)

\(=x\left(x+6\right)-\left(x+6\right)\)

\(=\left(x-1\right)\left(x-6\right)\)