a) 2x^2 -  2xy - 5x +5y

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

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

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

b)8x²  +4xy-2ax-ay

=(8x² +4xy) -(2ax+ay)

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

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

c)=x(x² -4x +4)

=x(x-2)²

d)=16- (x² -2xy +y^2)

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

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

các câu còn lại tg tự

chúc bn hok tốt

\(x^3+3x^2+6x+4=\left(x^3+x^2\right)+\left(2x^2+2x\right)+\left(4x+4\right)\)

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

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

a)   \(x^3+3x^2+6x+4\)

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

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

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

b) \(3a^2c^2+bd+3abc+acd\)

\(=\left(3a^2c^2+acd\right)+\left(3abc+bd\right)\)

\(=ac\left(3ac+d\right)+b\left(3ac+d\right)\)

\(=\left(ac+b\right)\left(d+3ac\right)\)

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

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

d) \(x^2+y^2-x^2y^2+xy-x-y\)

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

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

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

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

e)  \(a^6-b^6=\left(a^3-b^3\right)\left(a^3+b^3\right)=\left(a-b\right)\left(a^2+ab+b^2\right)\left(a+b\right)\left(a^2-ab+b^2\right)\)

a ) \(x^3+3x^2+6x+4\)

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

\(=\left(x+1\right)^3+3\left(x+1\right)\)

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

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

b ) \(3a^2c^2+bd+3abc+acd\)

\(=\left(3a^2c^2+3abc\right)+\left(bd+acd\right)\)

\(=3ac\left(ac+b\right)+d\left(ac+b\right)\)

\(=\left(3ac+d\right)\left(ac+b\right)\)

c ) \(3a^2-6ab+3b^2-12c^2\)

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

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

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

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

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

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

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

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

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

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

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

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

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

e ) \(a^6-b^6=\left(a^3\right)^2-\left(b^3\right)^2=\left(a^3-b^3\right)\left(a^3+b^3\right)\) \(=\left(a-b\right)\left(a^2+ab+b^2\right)\left(a+b\right)\left(a^2-ab+b^2\right)\)

a, \(x^3+3x^2+6x+4\)

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

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

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

e, \(a^6-b^6\)

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

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

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

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

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

b) \(8x^2+4xy-2ax-ay\)

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

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

c) \(x^3-4x^2+4x\)

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

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

d) \(2xy-x^2-y^2+16\)

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

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

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

e) \(x^2-y^2-2yz-z^2\)

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

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

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

g) \(3a^2-6ab+3b^2-12c^2\)

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

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

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

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

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

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

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

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

2:

a: \(x^2-12x+20\)

\(=x^2-2x-10x+20\)

=x(x-2)-10(x-2)

=(x-2)(x-10)

b: \(2x^2-x-15\)

=2x^2-6x+5x-15

=2x(x-3)+5(x-3)

=(x-3)(2x+5)

c: \(x^3-x^2+x-1\)

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

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

d: \(2x^3-5x-6\)

\(=2x^3-4x^2+4x^2-8x+3x-6\)

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

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

e: \(4y^4+1\)

\(=4y^4+4y^2+1-4y^2\)

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

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

f; \(x^7+x^5+x^3\)

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

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

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

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

g: \(\left(x^2+x\right)^2-5\left(x^2+x\right)+6\)

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

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

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

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

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

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

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

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

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

\(=\left(x+1\right)^2\left[\left(x+1\right)^2-4\right]\)

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

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

i: \(x^2+4xy+4y^2-4\left(x+2y\right)+3\)

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

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

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

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

j: \(x\cdot\left(x+1\right)\left(x+2\right)\left(x+3\right)-3\)

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

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

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

a) 25 - x² + 4xy - 4y² = 25 - (x² - 4xy + 4y²) = 5² - (x - 2y)² = (5 + x - 2y)(5 - x +2y) = (x - 2y + 5)(2y - x + 5)

b) 3a²c² + bd + 3abc + acd = (3a²c²​ + 3abc) + (bd + acd) = 3ac(ac + b) + d (ac + b) = (ac + b)(3ac + d)

c) x³ - 2x² - x + 2 = x²(x - 2) - (x - 2) = (x - 2)(x² - 1) = (x - 2)(x - 1)(x + 1)

d) a⁴ + 5a³ + 15a - 9 = (a⁴ + 3a²) + (5a³ + 15a) - (3a² + 9) = a²(a² + 3) + 5a(a² + 3) - 3(a² + 3) = (a² + 3)(a² + 5a - 3)

4x^2=28x+49

4x^2+28X+49

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

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

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

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

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

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

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

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

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

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