a) 10x + 15y = 5(2x + 3y)

b) x² - 2xy - 4 + y²

= (x² - 2xy + y²)  - 4

= (x - y)² - 2²

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

c) x(x + y) - 3x - 3y

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

= (x - 3)(x + y)

a, \(10x+15y=5\left(2x+3y\right)\)

b, \(x^2-2xy-4+y^2=\left(x-y\right)^2-4=\left(x-y-2\right)\left(x-y+2\right)\)

c, \(x\left(x+y\right)-3x-3y=x\left(x+y\right)-3\left(x+y\right)=\left(x-3\right)\left(x+y\right)\)

a)3xy+x+15y+5

 =(3xy+x)+(15y+5)

 =x(3y+1)+5(3y+1)

 =(x+y)(3y+1)

b)2x+2y+x²-y²

 =tôi đang nghĩ

a, 3xy+x+15y+5

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

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

b, 2x+2y+x²-y²

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

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

\(1,=\left(x-3\right)\left(x+3\right)\\ 2,=\left(x-y\right)\left(5+a\right)\\ 3,=\left(x+3\right)^2\\ 4,=\left(x-y\right)\left(10x+7y\right)\\ 5,=5\left(x-3y\right)\\ 6,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

bạn gõ lại công thức cho rõ đi, khó đọc quá

a) 5x^2 + 6xy + y^2

=5x²+5xy+xy+y²

=5x.(x+y)+y.(x+y)

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

b) x^2 + 2xy - 15y^2.

=x²-3xy+5xy-15y²

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

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

c) (x-y)^2 + 4(x-y) - 12

=(x-y)²+4(x-y)+4-16

=(x-y+2)²-16

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

=(x-y-2)(x-y+6)

d) x^3 - 2x - 4.

=x³+2x²+2x-2x²-4x-4

=x.(x²+2x+2)-2.(x²+2x+2)

=(x²+2x+2)(x-2)

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

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

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

b) \(x^3-x+3x^2y+3xy^2+y^3-y\)

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

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

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

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

Bài 1: 

\(=3x^3y-6x^2y^2+15xy\)

Bài 2: 

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

\(x^2+2xy-25+y^2\\ =\left(x^2+2xy+y^2\right)-5^2\\ =\left(x+y\right)^2-5^2\\ =\left(x+y-5\right)\left(x+y+5\right)\)

a: =5(2x+3y)

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

a: x^2+4xy-21y^2

\(=x^2+7xy-3xy-21y^2\)

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

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

b: \(5x^2+6xy+y^2\)

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

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

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

c: \(x^2+2xy-15y^2\)

\(=x^2+5xy-3xy-15y^2\)

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

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

d: \(x^2-7xy+10y^2\)

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

=x(x-2y)-5y(x-2y)

=(x-2y)(x-5y)

a) \(x^2+4xy-21y^2\)

\(=x^2+7xy-3xy-21y^2\)

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

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

b) \(5x^2+6xy+y^2\)

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

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

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

c) \(x^2+2xy-15y^2\)

\(=x^2+5xy-3xy-15y^2\)

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

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

d) \(x^2-7xy+10y^2\)

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

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

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

a) x² + 4xy - 21y²

= x² - 3xy + 7xy - 21y²

= (x² - 3xy) + (7xy - 21y²)

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

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

b) 5x² + 6xy + y²

= 5x² + 5xy + xy + y²

= (5x² + 5xy) + (xy + y²)

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

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

c) x² + 2xy - 15y²

= x² + 2xy + y² - 16y²

= (x² + 2xy + y²) - 16y²

= (x + y)² - (4y)²

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

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

d) x² - 7xy + 10y²

= x² - 2xy - 5xy + 10y²

= (x² - 2xy) - (5xy + 10y²)

= x(x - 2y) - 5y(x - 2y)

= (x - 2y)(x - 5y)

a)2x^2+xy-y^2-x+2y-1

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

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

=2a^2+ab-b^2         với a=x,b=y-1

=2a^2+2ab-ab-b^2

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

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