a. 3x - 3 + 5(x - 1)

= 3(x - 1) + 5(x - 1)

= (3 + 5)(x - 1)

= 8(x - 1)

b. x² - 25 + y² - 2xy

= (x² - 2xy + y²) - 25

= (x - y)² - 5²

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

c. x² + 2xy - 16a² + y²

= (x² + 2xy + y²) - 16a²

= (x + y)² - (4a)²

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

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

\(3x^3+6x+3-3y^2=3\left[\left(x^2+2x+1\right)-y^2\right]=3\left[\left(x+1\right)^2-y^2\right]=3\left(x-y+1\right)\left(x+y+1\right)\)

\(a,=\left(2y^2-1\right)\left(2y^2+1\right)\\ b,=\left(x+y\right)^2-9=\left(x+y+3\right)\left(x+y-3\right)\)

Lời giải:
a. $4y^4-1=(2y^2)^2-1^2=(2y^2-1)(2y^2+1)$

b. $x^2+2xy-9+y^2=(x^2+2xy+y^2)-9$

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

a) \(7\left(3x-2\right)+y\left(3x-2\right)=\left(3x-2\right)\left(7+y\right)\)

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

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

a. (3x - 2)(7+y)

b. (x - y)(x - 3)

c. (x-3y)²

a. 7(3x - 2) + y(3x - 2)

= (7 + y)(3x - 2)

b. x(y - x) - 3(x - y)

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

= (x + 3)(y - x)

c. x² - 6xy + 9y²

= x² - 3y.x.2 + (3y)²

= (x - 3y)²

\(x^2+2xy+7x+7y+y^2+10\)

\(=\left(x^2+2xy+y^2\right)+\left(7x+7y\right)+\frac{49}{4}-\frac{9}{4}\)

\(=\left(x+y\right)^2+7\left(x+y\right)+\frac{49}{4}-\frac{9}{4}\)

\(=\left(x+y+\frac{7}{2}\right)^2-\frac{9}{4}\)

\(=\left(x+y+\frac{7}{2}-\frac{3}{2}\right)\left(x+y+\frac{7}{2}+\frac{3}{2}\right)\)

\(=\left(x+y+2\right)\left(x+y+5\right)\)

b)Ta có: x²y+xy²+x+y=2010

<=>xy.x+xy.y+x+y=2010

<=>11x+11y+x+y=2010

<=>12(x+y)=2010

<=>x+y=167,5

=>(x+y)²=28056,25

<=>x²+y²+2xy=28056,25

<=>x²+y²=28034,25

\(\left(x+y\right)^2+7\left(x+y\right)+\frac{49}{4}-\frac{9}{4}\)

\(=\left(x+y\right)^2+2\left(x+y\right).\frac{7}{2}+\left(\frac{7}{2}\right)^2-\frac{9}{4}\)

\(=\left(x+y+\frac{7}{2}\right)^2-\frac{9}{4}\)   (áp dụng HĐT số 1)

\(=\left(x+y+\frac{7}{2}\right)^2-\left(\frac{3}{2}\right)^2\)  

\(=\left(x+y+\frac{7}{2}-\frac{3}{2}\right)\left(x+y+\frac{7}{2}+\frac{3}{2}\right)\)(áp dụng HĐT số 3)

\(=\left(x+y+2\right)\left(x+y+5\right)\)

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

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

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

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

a) \(7x^2+34x-5=7x\left(x+5\right)-1\left(x+5\right)\)

\(=\left(x+5\right)\left(7x-1\right)\)

b) \(12a^2-3ab+8ac-2bc=3a\left(4a-b\right)+2c\left(4a-b\right)\)

\(=\left(4a-b\right)\left(3a+2c\right)\)

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

Phân tích đa thức thành phân tử:

a) 

b) 

a) \(=\left(3ax+3bx\right)-\left(4by+4ay\right)=3x\left(a+b\right)-4y\left(a+b\right)=\left(a+b\right)\left(3x-4y\right)\)

b) \(=3\left[\left(x^2-2xy+y^2\right)-4t^2\right]=3\left[\left(x-y\right)^2-4t^2\right]=3\left(x-y-2t\right)\left(x-y+2t\right)\)

c) Không phân tích được