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1 tháng 7 2019

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

Bài 3:

a) Ta có: \(x^2+4xy-21y^2\)

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

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

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

b) Ta có: \(5x^2+6xy+y^2\)

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

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

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

c) Ta có: \(x^2+2xy-15y^2\)

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

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

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

d) Ta có: \(\left(x-y\right)^2+4\left(x-y\right)-12\)

\(=\left(x-y\right)^2+6\left(x-y\right)-2\left(x-y\right)-12\)

\(=\left(x-y\right)\left(x-y+6\right)-2\left(x-y+6\right)\)

\(=\left(x-y+6\right)\left(x-y-2\right)\)

e) Ta có: \(x^2-7xy+10y^2\)

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

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

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

f) Ta có: \(x^2yz+5xyz-14yz\)

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

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

\(=yz\left[x\left(x+7\right)-2\left(x+7\right)\right]\)

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

22 tháng 10 2023

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)

22 tháng 10 2023

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) \(x^2-7xy+10y^2\)

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

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

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

18 tháng 10 2020

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

18 tháng 10 2020

câu a làm sao tahc thành-6x+x đc vậy bạn

29 tháng 7 2018

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)\(5x^2+6xy+y^2\)

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

=\(5x^{ }\left(x+y\right)+y\left(x+y\right)\)

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

29 tháng 7 2018

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

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

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

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

27 tháng 7 2016

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

4 tháng 11 2017

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)

4 tháng 11 2017

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)

7 tháng 10 2017

\(a,x^2+4xy-21y^2\\ =x^2+7xy-3xy-21y^2\\ =x\left(x+7y\right)-3y\left(x+7y\right)\\ =\left(x+7y\right)\left(x-3y\right)\\ b,5x^2+6xy+y^2\\ =5x^2+5xy+xy+y^2\\ =5x\left(x+y\right)+y\left(x+y\right)\\ =\left(x+y\right)\left(5x+y\right)\\ c.x^2+2xy-15y^2\\ =x^2+5xy-3xy-15y^2\\ =x\left(x+5y\right)-3y\left(x+5y\right)\\ =\left(x+5y\right)\left(x-3y\right)\)

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