a ) ( 6x + 1 )² + ( 6x - 1 )²  - 2 . ( 6x + 1 )( 6x - 1 )

= ( 6x + 1 )² - 2 . ( 6x + 1 )( 6x - 1 ) + ( 6x - 1 )²

= ( 6x + 1 - 6x + 1 )²

= 2² = 4

b ) x . ( 2x² - 3 ) - x² . ( 5x + 1 ) + x²

= 2x³ - 3x - 5x³ - x² + x²

= ( 2x³ - 5x³ ) - 3x - ( x² - x² )

= - 3x³ - 3x

= - 3x . ( x² + 1)

a)

=> 6x^2 - 3x + 4x - 2 - 6x^2 + 12x = 3 

=> 13x          = 3 + 2 

=> 13x           = 5 

=> x              = 5/13 

b) ( 5x + 1 )( 6x - 2 ) = 30 x (x + 1/2 )

=> 30x^2 - 10x + 6x - 2 = 30x^2 + 15x 

=>  30x^2  - 4x - 30x^2 - 15x = 2 

=> - 19x                        = 2 

=> x                               = -2/19

b. 6x(x - 5) - x(6x + 3)

= x(6x - 30) - x(6x + 3)

= x(6x - 30 - 6x - 3)

= x(-33)

= -33x

\(1,\\ a,=-35x^5y^4z\\ b,=6x^2-30x-6x^2-3x=-33x\\ c,=x^3-9x^2-2x^2+18x-x+9=x^3-11x^2+17x+9\\ 2,\\ A\left(x\right)+B\left(x\right)=10-2x+4x^3-5x^2-10x^3-5x+6x^2-20\\ =-6x^3+x^2-7x-10\\ A\left(x\right)-B\left(x\right)=10-2x+4x^3-5x^2+10x^3+5x-6x^2+20\\ =14x^3-11x^2+3x+30\\ 3,\\ a,M\left(x\right)=5x+20=0\\ \Leftrightarrow x=-4\\ b,N\left(x\right)=100x^2-49=0\\ \Leftrightarrow\left(10x-7\right)\left(10x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{10}\\x=-\dfrac{7}{10}\end{matrix}\right.\\ c,P\left(x\right)=3x-15=0\\ \Leftrightarrow x=5\)

Bài 1;

a)\(5x^3yz.\left(-7x^2y^3\right)=-35.x^5y^4z\)

b)\(6x\left(x-5\right)-x\left(6x+3\right)=6x^2-30x-6x^2-3x=-33x\)

c) \(\left(x-9\right)\left(x^2-2x-1\right)=x^3-2x^2-x-9x^2+18x+9=x^3-11x^2+17x+9\)

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

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

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

\(=4\)

\(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)

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

\(=\left(2x^3-5x^3\right)+\left(x^2-x^2\right)-3x\)

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

\(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)

\(=3x^2-6x-5x+5x^2-8x^2+24\)

\(=\left(3x^2+5x^2-8x^2\right)-\left(6x+5x\right)+24\)

\(=-11x+24\)