C = ( x² - 2x + 4 )( x + 2 ) - ( x - 2 )³ - 6( x - 1 )( x + 1 )

= x³ + 8 - ( x³ - 6x² + 12x - 8 ) - 6( x² - 1 )

= x³ + 8 - x³ + 6x² - 12x + 8 - 6x² + 6

= -12x + 22

Với x = 11/6

C = -12.11/6 + 22

    = -22 + 22 

    = 0

\(C=\left(x^2-2x+4\right)\left(x+2\right)-\left(x-2\right)^3-6\left(x-1\right)\left(x+1\right)\)

\(C=x^3+2^3-\left(x-2\right)^3-6\left(x^2-1\right)\)

\(C=x^3+2^3-\left(x^3-6x^2+12x-8\right)-6x^2+6\)

\(C=x^3+8-x^3+6x^2-12x+8-6x^2+6\)

\(C=22-12x\)

Thay x = 11/6 vào ta có : \(22-12\cdot\frac{11}{6}=22-22=0\)

 .\(a\left(b^2+c^2\right)+b\left(c^2+a^2\right)+c\left(a^2+b^2\right)-2abc-a^3-b^3-c^3\)

=\(a\left(b^2-2bc+c^2-a^2\right)+b\left(a^2+2ac+c^2-b^2\right)+c\left(a^2-2ab+b^2-c^2\right)\)

=\(a\left[\left(b-c\right)^2-a^2\right]+b\left[\left(a+c\right)^2-b^2\right]+=c\left[\left(a-b^2\right)-c^2\right]\)

=\(a\left(c-b+a\right)\left(a+b-c\right)+b\left(a+c-b\right)\left(a+b+c\right)+c\left(a-b+c\right)\left(a-b-c\right)\)

=\(\left(a+c-b\right)\left[a\left(c-b+a\right)+b\left(a+b+c\right)+c\left(a-b-c\right)\right]\)

=\(\left(a+c-b\right)\left(b+a-c\right)\left(c+b-a\right)\)

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

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

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

X^3-3x^2+3x^2+3x-1

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

=x^3+3x-1

\(2.\left(3x-1\right).\left(2x-5\right)-\left(4x-1\right).\left(3x-2\right)\)

\(\Leftrightarrow6x-2.\left(2x-5\right)-12x^2-8x-3x+2\)

\(\Leftrightarrow12x^2-30x-4x+10-12x^2-11x+2\)

\(\Leftrightarrow-45x+12\)

2( 3x - 1 )( 2x - 5 ) - ( 4x - 1 )( 3x - 2 )

= 2( 6x² - 17x + 5 ) - ( 12x² - 11x + 2 )

= 12x² - 34x + 10 - 12x² + 11x - 2

= -23x + 8 

( 3x² - 2x + 1 )( 3x² + 2x + 1 ) - ( 3x² + 1 )²

= [ ( 3x² + 1 ) - 2x ][ ( 3x² + 1 ) + 2x ] - ( 3x² + 1 )²

= ( 3x² + 1 )² - 4x² - ( 3x² + 1 )²

= -4x²

\(M=18+4x-8y+6xy+5x^2+10y^2\)

\(=\left(x^2+6xy+9y^2\right)+\left(4x^2+4x+1\right)+\left(y^2-8y+16\right)+1\)

\(=\left(x+y\right)^2+4\left(x+\frac{1}{2}\right)^2+\left(y-4\right)^2+1\)

Có \(\left(x+y\right)^2\ge0\forall xy\)

\(4\left(x+\frac{1}{2}\right)^2\ge0\forall x\)

\(\left(y-4\right)^2\ge0\forall y\)

\(\Rightarrow M\ge1\forall x,y\)

hay \(M>0\forall x,y\)

giải trên cymath.com í

3 ( 1 - 2x ) ( 5 - 3x )

= ( 3 - 6x ) ( 5 - 3x )

= 15 - 9x - 30x + 18x²

= 18x² - 39x + 15

3(1-2x)(5-3x)

=3(5-10x-3x+6x²)

=15-30x-9x+18x²

=15-39x+18x²