b: \(2x^2-7xy+3y^2+x-3y\)

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

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

\(=\left(x-3y\right)\left(2x-y+1\right)\)

Lời giải:
a.

Đặt $2a^2+5ab-3b^2-7b-2=(a+mb+n)(2a+pb+k)$ với $m,n,p,k$ nguyên 

$\Leftrightarrow 2a^2+5ab-3b^2-7b-2=2a^2+ab(2m+p)+mpb^2+a(k+2n)+b(km+np)+kn$ 

Đồng nhất hệ số:

\(\left\{\begin{matrix} 2m+p=5\\ mp=-3\\ k+2n=0\\ km+np=-7\\ kn=-2\end{matrix}\right.\)

Giải hpt này ta thu được $m=3; n=1; p=-1; k=-2$

Vậy $2a^2+5ab-3b^2-7b-2=(a+3b+1)(2a-b-2)$

b. Đa thức không phân tích được thành nhân tử

lm theo pp đồng nhất hệ số ạ

b: Ta có: \(2x^2-7xy+3y^2+x-3y\)

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

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

\(=\left(x-3y\right)\left(2x-y+1\right)\)

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

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

=(x+y)^3+1

=(x+y+1).[(x+y)^2+(x+y)+1]      

a, \(x^2\) + 4\(x\) - y² + 4

= (\(x^2\) + 4\(x\) + 4) - y²

= (\(x\) + 2)² - y²

= (\(x\) + 2 - y)(\(x\) + 2 + y)

b, 2\(x^2\) - 18

= 2.(\(x^2\) -9)

= 2.(\(x\) -3).(\(x\) + 3)

c, \(x^3\) - \(x^2\) - \(x\) + 1

= (\(x^3\) + 1) - (\(x^2\) +  \(x\))

= (\(x\) + 1)(\(x\)² - \(x\) + 1) - \(x\).(\(x\) + 1)

=(\(x\) + 1).(\(x^2\) - \(x\) + 1  - \(x\))

= (\(x\) + 1).(\(x\) - 1)²

e) \(8\left(x+3y\right)-16x\left(x+3y\right)=\left(x+3y\right)\left(8-16x\right)=8\left(x+3y\right)\left(1-2x\right)\)

f) \(4x^2\left(x+1\right)+2x^2\left(x+1\right)=\left(x+1\right)\left(4x^2+2x^2\right)=6x^2\left(x+1\right)\)

g) \(3\left(x-y\right)-5x\left(y-x\right)=3\left(x-y\right)+5x\left(x-y\right)=\left(3+5x\right)\left(x-y\right)\)

mn ơiiiiiiiiiiiii

câu này phải ko

\(2x^2-7xy+3y^2+5xz-5yz+2z^2=\left(2x^2+2z^2\right)+\left(5xz-5yz\right)-\left(7xy-3y^2\right)\)

\(=2\left(x^2+z^2\right)+5z\left(x-y\right)-y\left(7x-3y\right)\)

\(2x^2-7xy+3y^2+5xz-5yz+2z^2\)

\(=\left(2x^2+4xz-6xy\right)-\left(xy+2yz-3y^2\right)+\left(2z^2+xz-3yz\right)\)

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

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

g: \(3\left(x-y\right)-5x\left(y-x\right)=\left(x-y\right)\left(5x+3\right)\)

f: \(4x^2\left(x+1\right)+2x^2\left(x+1\right)\)

\(=6x^2\left(x+1\right)\)

f: \(4x^2\left(x+1\right)+2x^2\left(x+1\right)=6x^2\left(x+1\right)\)

g: \(3\left(x-y\right)-5x\left(y-x\right)=\left(x-y\right)\left(5x+3\right)\)

câu f có ( x+1) là nhân tử chung

câu g đổi dấu - thành + thì (y-x) sẽ thành (x-y)

e: \(8\left(x+3y\right)-16x\left(x+3y\right)=8\left(x+3y\right)\left(1-2x\right)\)

f: \(4x^2\left(x+1\right)+2x^2\left(x+1\right)=6x^2\left(x+1\right)\)