2) \(5x^2+6xy+y^2\) 

 \(=9x^2+6xy+y^2-4x^2\)  

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

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

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

3) \(x^2+2xy-15y^2=x^2+2xy+y^2-16y^2\) 

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

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

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

hc tốt

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)

bạn viết lại đề đi, có số mũ, xuống dòng chứ thế này ai mà giải được

a) \(x^2+4xy-21y^2=x^2-3xy+7xy-21y^2=x\left(x-3y\right)+7y\left(x-3y\right)\)\(=\left(x-3y\right)\left(x+7y\right)\)

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) \(x^2-7xy+10y^2\)

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

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

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

d)\(x^2+2xy-15y^2\)

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

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

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

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)

a)3x²-5x-2=3x²-6x+x-2

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

=(3x+1)(x-2)

b)x²-7xy-10y²=x²-2xy-5xy-10y²

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

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

c)c) x² +4xy-21y²=x²+7xy-3xy-21y²

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

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

d) 5x² +6xy+y²=5x²+5xy+xy+y²

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

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

e) x² +2xy-15y²=x²+5xy-3xy-15y²

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

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

CHÚC BẠN HỌC TỐT

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

a) 3x² +9x - 30

= 3(x² + 3x -10) = 3[(x² -2x)+(5x-10)]

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

b) x² -9x + 18 = (x² - 3x) - (6x-18)

= (x-3)(x-6)

c) x² -7x +12 = (x² -3x)-(4x-12)

= (x-3)(x-4)

d) x² + 4xy -21y² = (x² -3xy)+(7xy - 21y²)

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

e) 5x² + 6xy +y²

= (5x² + 5xy)+(xy+y²)

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

f) x² +2xy-15y² = (x² - 3xy)+(5xy-15y²)

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

g) x² -7xy+10y² = (x² - 2xy)-(5xy-10y²)

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

h) 4x⁴ +1 = [(2x²)² + 4x² + 1 ] - 4x²

= (2x² +1)² -(2x)²

= (2x² + 1-2x)(2x² +1+2x)

i) x⁴ + 324 = [x⁴ + 36x² + 18²] - 36x²

= (x² + 18)² - (6x)²

= (x² -6x +18)(x² +6x+18)

3x²+9x-30

=3(x2+3x-10)

=3(x2+5x-2x-10)

=3[(x2+5x)-(2x+10)]

=3[x(x+5)+2(x+5)]

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