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

\(c,3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3.\left(\left(a-b\right)^2-\left(2c\right)^2\right)\)

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

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

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

\(e,a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b\right)\left(a+b-c\right)\)

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

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

\(h,x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x-1\right)\left(x^2-16\right)=\)

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

a) Ta có : x² - y² - 2x + 2y

= (x² - y²) - (2x - 2y)

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

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

a, x² - y² - 2x + 2y

= ( x² - y² ) - ( 2x - 2y )

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

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

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

= 2. ( x + y ) - x.( x + y )

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

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

\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left(a-b\right)^2-3\left(2c\right)^2=3\left(a-b+2c\right)\left(a-b-2c\right)\) \(x^2-25+y^2+2xy=\left(x+y\right)^2-25=\left(x+y-5\right)\left(x+y+5\right)\)

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

\(x^2-2x+1-4y^2-4y-1=\left(x-1\right)^2-\left(2y+1\right)^2=\left(x+2y\right)\left(x-2y-2\right)\)\(x^2\left(x-1\right)-16\left(x-1\right)=\left(x-1\right)\left(x^2-16\right)=\left(x-1\right)\left(x+4\right)\left(x-4\right)\) \(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(y-x\right)\left(x^2-9\right)\left(y-x\right)\left(x-3\right)\left(x+3\right)\)

a) Ta có: 10(x-y)-8y(y-x)

\(=10\left(x-y\right)+8y\left(x-y\right)\)

\(=2\left(x-y\right)\left(5+4y\right)\)

d) Ta có: \(x^2y-x^3-9y+9x\)

\(=x^2\left(y-x\right)-9\left(y-x\right)\)

\(=\left(y-x\right)\left(x^2-9\right)\)

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

e) Ta có: \(2x+2y-x^2-xy\)

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

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

f) Ta có: \(x^2-25+y^2+2xy\)

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

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

g) Ta có: \(x^2-2x-4y^2-4y\)

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

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

h) Ta có: \(x^2\left(x-1\right)+16\left(1-x\right)\)

\(=x^2\left(x-1\right)-16\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2-16\right)\)

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

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

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

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

b)\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)\)\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)

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

a) x²-y²-2x+2y

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

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

b) 2x + 2y - x² -xy

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

=(x+y)(2-x)

c) 3a² - 6ab + 3b² - 12c²

= 3(a²+b²) -3(2ab+4c²)

= 3(a²+b²-2ab-4c²)

d) x² - 25 + y² + 2xy

= x² + 2xy + y² -25

= (x+y)² - 5²

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

e) x²y - x³ - 9y + 9x

= (9x - x³)+(x²y -9y)

= x(9-x²)+y(x² - 9)

= x(9-x²)-y(9-x²)

= (9-x²)(x-y)

f) x²-2x-4y²-4y

= x²-4y²-2(x+2y)

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

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

câu g trùng với câu e

h) x²(x-1)+16(1-x)

= x²(x-1)-16(x-1)

= (x²-16)(x-1)

= (x+4)(x-4)(x-1)

Bài làm:

a) x² - y² - 2x + 2y = (x - y)(x + y) - (2x - 2y)

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

= [(x + y) - 2].(x - y)

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

c)3a² - 6ab + 3b² - 12c² = (3a² - 6ab + 3b²) - 12c²

= 3(a² - 2ab + b²) - 12c²

= 3[(a - b)²] - 12c²

= 3[(a - b)² - 4c²]

= 3[(a - b)² - (2c)²]

= 3[(a - b - c) - (a - b + c)]

= 3(a - b - c - a + b - c)

= 3(-2c)

= -6c

d)x² - 5 + y² + 2xy = (x² + 2xy + y²) - 5

= (x + y)² - 5

= (x + y)² -(\(\sqrt{5}\))²

= (x + y - \(\sqrt{5}\)) - (x + y + \(\sqrt{5}\))

= x + y - \(\sqrt{5}\) - x - y -\(\sqrt{5}\)

= -2\(\sqrt{5}\)

e) a² + 2ab + b² - ac - bc = (a² + 2ab + b²) - (ac + bc)

= (a + b)² - c(a + b)

= [(a + b) - c].(a + b)

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

Còn câu b) và câu f) Vàng sẽ nghĩ sau :v

Tiếp câu f luôn !

\(x^2-2x-4y^2-4y\)

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

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

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

l

a: 2x^2y-50xy=2xy(x-25)

b: 5x^2-10x=5x(x-2)

c: 5x^3-5x=5x(x^2-1)=5x(x-1)(x+1)

d: \(x^2-xy+x=x\left(x-y+1\right)\)

e: x(x-y)-2(y-x)

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

=(x-y)(x+2)

f: 4x^2-4xy-8y^2

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

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

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

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

f1: x^2ỹ-y^2+y

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

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