\(B=-10-x^2-6x\)

\(\Rightarrow B=-\left(x^2+6x+10\right)\)

\(\Rightarrow B=-\left(x^2+6x+9+1\right)\)

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

Vì \(\left(x+3\right)^2\ge0\forall x\)\(\Rightarrow\left(x+3\right)^2+1\ge1\)

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

=> Đpcm

B=\(-10-x^2-6x\)  

B=\(-x^2-6x-9-1\) 

B=\(-\left(x^2+6x+9\right)-1\)    

=\(-\left(x+3\right)^2-1\)   

Ta có : \(\left(x+3\right)^2\ge0\forall x\) 

\(-\left(x+3\right)^2\le0\) 

\(-\left(x+3\right)^2-1\le-1\)      

Vậy B luôn âm với mọi x 

(x+5)³-x³-125

=x³+5³-x³-5³

=0

1. \(\left(x+5\right)^3-x^3-125\)

\(=x^3+15x^2+75x+125-x^3-125\)

\(=15x^2+75x\)

2. \(x^3+6x^2+12x+8=0\)

\(\Leftrightarrow x^3+2x^2+4x^2+8x+4x+8=0\)

\(\Leftrightarrow x^2\left(x+2\right)+4x\left(x+2\right)+4\left(x+2\right)=0\)

\(\Leftrightarrow\left(x^2+4x+4\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left(x+2\right)^2\left(x+2\right)=0\)

\(\Leftrightarrow\left(x+2\right)^3=0\)

\(\Leftrightarrow x+2=0\Leftrightarrow x=-2\)

5x² - 5xy + 4y - 4x

= 5x ( x - y ) - 4 ( x - y )

= ( 5x - 4 ) ( x - y )

( x + y )³ + ( x - y )³

= 2x³ + 6xy²

= 2x ( x² + 3y² )

5 x^2 - 5xy + 4y - 4x 

= 5x ( x - y ) - 4 ( x - y ) 

= ( x - y ) ( 5x - 4 ) 

( x + y )^3 + ( x - y )^3 

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

= \(2x^3+6xy^2\) 

=\(2x\left(x^2+3y^2\right)\) 

a) \(5x\left(x-1\right)-3x\left(x-1\right)\)

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

b) \(x\left(x+y\right)-5x-5y\)

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

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

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

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

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

d) \(x^2+xy+x=x\left(x+y+1\right)\)

a. 5x ( x - 1 ) - 3x ( x - 1 )

= ( 5x - 3x ) ( x - 1 )

b. x ( x + y ) - 5x - 5y

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

= ( x - 5 ) ( x + y )

c. x ( x - y ) + y ( y - x )

= x ( x - y ) - y ( x - y )

= ( x - y )²

 d. x² + xy + x 

= x ( x + y + 1 )

làm ơn giúp mk

- 6x² - 9xy + 15x

= - 3x ( 3y + 2x - 5 )

2x ( x - 3 ) + y ( x - 3 ) + ( 3 - x )

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

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