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)

X²+4xy-21y²=(x²+4xy+4y²)-25y²=(x+2)²-(5y)²=(x+2-5y)(x+2+5y)

5x²+6xy+y²=9x²+6xy+y²-4x²=(3x+y)²-4x²=(3x+y+2x)(3x+y-2x)

(x-y)²+4(x-y)-12=(x-y+2)²-16=(x-y+2+4)(x-y+2-4)

x²-7xy+10y²=x²-7xy+\(\frac{49y^2}{4}-\frac{9y^2}{4}\)= \(\left(x-\frac{7}{2}\right)^2-\left(\frac{3y}{2}\right)^2\)=\(\left(x-\frac{7}{2}-\frac{3y}{2}\right)\left(x-\frac{7}{2}+\frac{3y}{2}\right)\)

x²+2xy-15y²=(x+y)²-16y²=(x+y-4y)(x+y+4y

f)\(x^2-5x-14=x^2-7x+2x-14=x\left(x-7\right)+2\left(x-7\right)=\left(x-7\right)\left(x+2\right)\)

i)\(x^2-7x+10=x^2-2x-5x+10=x\left(x-2\right)-5\left(x-2\right)=\left(x-5\right)\left(x-2\right)\)

h)\(x^2-7x+12=x^2-3x-4x+12=x\left(x-3\right)-4\left(x-3\right)=\left(x-4\right)\left(x-3\right)\)

g)\(x^2+6x+5=x^2+x+5x+5=x\left(x+1\right)+5\left(x+1\right)=\left(x+1\right)\left(x+5\right)\)

f)\(x^2-5x-14=x^2-7x+2x-14\)

                             \(=\left(x+2\right)\left(x-7\right)\)

i)\(x^2-7x+10=x^2-5x-2x+10\)

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

h)\(x^2-7x+12=x^2-4x-3x+12\)

                              \(=\left(x-3\right)\left(x-4\right)\)

g)\(x^2+6x+5=x^2+x+5x+5\)

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

f) \(x^2-5x-14\)

\(=x^2-7x+2x-14\)

\(=\left(x^2-7x\right)+\left(2x-14\right)\)

\(=x\left(x-7\right)+2\left(x-7\right)\)

\(=\left(x+2\right)\left(x-7\right)\)

i) \(x^2-7x+10\)

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

\(=\left(x^2-5x\right)-\left(2x-10\right)\)

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

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

h) \(x^2-7x+12\)

\(=x^2-3x-4x+12\)

\(=\left(x^2-3x\right)-\left(4x-12\right)\)

\(=x\left(x-3\right)-4\left(x-3\right)\)

\(=\left(x-4\right)\left(x-3\right)\)

g) \(x^2+6x+5\)

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

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

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

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

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)

Ta có : 5x² + 6xy + y²

= 5x² + 5xy + xy + y²

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

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

a) \(x^2-5x+6=x^2-2x-3x+6=\left(x-2\right)\left(x-3\right)\)

b)\(3x^2+9x-30=3x^2-6x+15x-30=3\left(x-2\right)\left(x+5\right)\)

c)\(x^2-7x+12=x^2-3x-4x+12=\left(x-3\right)\left(x-4\right)\)

d)\(x^2-7x+10=x^2-2x-5x+10=\left(x-2\right)\left(x-5\right)\)

a) \(x^2-5x+6=x^2-2x-3x+6=\left(x^2-2x\right)-\left(3x-6\right)\)

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

b) \(3x^2+9x-30=3\left(x^2+3x-10\right)=3\left(x^2-2x+5x-10\right)\)

\(=3\left[\left(x^2-2x\right)+\left(5x-10\right)\right]=3\left[x\left(x-2\right)+5\left(x-2\right)\right]\)

\(=3\left(x-2\right)\left(x+5\right)\)

c) \(x^2-7x+12=x^2-3x-4x+12=\left(x^2-3x\right)-\left(4x-12\right)\)

\(=x\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-4\right)\)

d) \(x^2-7x+10=x^2-2x-5x+10=\left(x^2-2x\right)-\left(5x-10\right)\)

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

a,\(x^2-5x+6=x^2-2x-3x+6 =x(x-2)-3(x-2) =(x-2)(x-3)\)

b,\(3x^2+9x-30=3x^2+15x-6x-30=3x(x+5)-6(x+5)=(x+5)(3x-6)\)

c,\(x^2-7x+12=x^2-4x-3x+12=x(x-4)-3(x-4)=(x-4)(x-3)\)

d,\(x^2-7x+10=x^2-2x-5x+10=x(x-2)-5(x-2)=(x-2)(x-5)\)

Hok tốt !!!!!!!!!!

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

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

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

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

1.Phân tích thành nhân tử ( phương pháp nhóm nhiều hạng tử )

a. x^3 + 2x^2 - xy - 2y

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

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

b. xy - 5x + 3y^2 - 15y

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

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

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

c.2xy + 6x + y^2 + 3y

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

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

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

a) \(x^3+2x^2-xy-2y\)

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

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

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

\(=\left(x+2\right)\left(x+\sqrt{y}\right)\left(x-\sqrt{y}\right)\)

a) \(x^3+2x^2-xy-2y\)

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

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

\(=\left(x+2\right)\left(x-\sqrt{y}\right)\left(x+\sqrt{y}\right)\)

b) \(xy-5x+3y^2-15y\)

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

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

c) \(2xy+6x+y^2+3y\)

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

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

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

b) \(25-x^2+4xy-4y^2=25-\left(x-2y\right)^2=\left(5-x+2y\right)\left(5+x-2y\right)\)

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

d) \(y^2\left(x-1\right)-7y^3+7xy^3\)

\(=y^2\left(x-1-7y+7xy\right)\)

\(=y^2\left[\left(x-1\right)-7y\left(1-x\right)\right]=y^2\left(x-1\right)\left(1+7y\right)\)

a)

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

b)

 \(25-x^2+4xy-4y^2\\ =25-\left(x^2-4xy-4y^2\right)\\ =5^5-\left(x-y\right)^2\\ =\left(5+x-y\right)\left(5-x+y\right)\)

a) \(x^2-xy+x-y\)

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

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

b) \(x^2+5x+6\)

\(=x^2+2x+3x+6\)

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

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

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

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

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