\(3m^2-2m-1\)

\(=3m^2-3m+m-1\)

\(=3m\left(m-1\right)+\left(m-1\right)\)

\(=\left(m-1\right)\left(3m+1\right)\)

\(3m^2-2m-1\)

\(=3m^2+m-3m-1\)

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

\(=m\left(3m+1\right)-\left(3m+1\right)\)

\(=\left(m-1\right)\left(3m+1\right)\)

\(2m^2+10m+8\)

\(=2\left(m^2+5m+4\right)\)

\(=2\left(m^2+4m+m+4\right)\)

\(=2\left(m+4\right)\left(m+1\right)\)

=2m²+8m+2m+8

=(2m²+2m)+(8m+8)

=2m(m+1)+8(m+1)

=(m+1)(2m+8)

=(m+1)2(m+4)

=2(m+1)(m+4)

HT~

a^3m+2a^2m+a^m = a^m(a^2m+2a^m+1) = a^m[(a^m)²+2a^m+1] = a^m(a^m+1)²

Ta có :

a^3m+2a^2m+a^m 

= a^m(a^2m+2a^m+1)

= a^m[(a^m)²+2a^m+1]

= a^m(a^m+1)²

\(a^{3m}+2a^{2m}+a^m\)

\(\Leftrightarrow a^m\left(a^{2m}+2a^m+1\right)\)

\(\Leftrightarrow a^m\left[\left(a^m\right)^2+2a^m+1\right]\)

\(\Leftrightarrow a^m\left(a^m+1\right)^2\)

\(\Leftrightarrow a^m\left(a^m+1\right)\left(a^m+1\right)\)

giúp me

\(=\left(m-n\right)\left(m+n\right)-2\left(m+n\right)=\left(m+n\right)\left(m-n-2\right)\)

\(m^2-n^2-2m-2n=\left(m^2-n^2\right)-\left(2m+2n\right)=\left(m-n\right)\left(m+n\right)-2\left(m+n\right)=\left(m+n\right)\left(m-n-2\right)\)

a) 9x² - 25

= (3x)² - 5²

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

b) y³ + 6y² + 9y

= y(y² + 6y + 9)

= y(y² + 2.y.3 + 3²)

= y(y + 3)²

c) m² - n² - 2m + 1

= (m² - 2m + 1) - n²

= (m - 1)² - n

= (m - 1 - n)(m - 1 + n)

= (m - n - 1)(m + n - 1)

B1:

[(m+n)+(2m-3n)]^2

= (m+n)^2 + 2(m+n)(2m-3n) + (2m-3n)^2

= m^2 +2mn +n^2 + 4m^2 - 6mn + 4mn - 6n^2 + 4m^2 - 12mn + 9n^2

= 9m^2 - 12mn + 4n^2
 

B2,3

 bn lm theo hdt ( a +b + c) ^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc nha

a)\(m+n+\left(2m-3n\right)^2=\left(3m-2n\right)^2\)

b)(x+y+z)^2 đã thành nhân tử 

c)(2x-y+3z)^2 đã thành nhân tử, too

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

e)\(8x^6-y^6=\left(2x^2-y^2\right)\left(4x^4+2x^2y^2+y^4\right)\)

g)\(\left(m+n\right)^3-\left(2m+3n\right)^3\)

\(=-\left(m+2n\right)\left(7m^2+19mn+13n^2\right)\)

a)     m m − 2 − m m + 2 m + 2 m m − 2 m = m + 2 m − 2

b)     3 5 − 3 m + 1 16 − m 2 m 2 + 2 m + 1 = 3 m − 12 5 ( m − 1 ) 16 − m 2 ( m + 1 ) 2 = − 3 ( m + 1 ) 5 ( m + 4 )

b) x^8+x^4+1

=x^8-x^2+x^4-x+x^2+x+1

=x^2(x^6-1)+x(x^3-1)+(x^2+x+1)

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

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

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

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

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

=(x^2+x+1)(x^6+x^3-x^5-x+1)

dung thi tick cho minh nha minh thu may tinh roi