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

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

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

\(=4\)

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

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

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

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

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

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

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

\(=-11x+24\)

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

\(=36x^2+12x+1+36x^2-12x+1-72x^2+2\)

\(=4\)

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

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

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

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

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

\(=-11x+24\)

a) (6x+1)² + (6x-1)² - 2(1+6x)(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

= -3x³ - 3x = -3x(x² -1) = -3x(x-1)(x+1)

c) 3x(x-2) - 5x(1-x) - 8(x² -3)

= 3x² - 6x - 5x + 5x² -8x² + 24

= -11x +24

a) (6x+1)² + (6x-1)² - 2(1+6x)(6x-1)

= (6x+1+6x-1)² 

=144x²

b) x(2x² -3) - x²(5x+1) +x²

=2x³ - 3x - 5x³ -x²+x²

=-3x³-3x

=-3x(x²+1)

c) 3(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

= (2²-1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

= (2⁴-1)(2⁴+1)(2⁸+1)(2¹⁶+1)

= (2⁸-1)(2⁸+1)(2¹⁶+1)

= (2¹⁶-1)(2¹⁶+1)

= 2³² -1

d) 3x(x-2) - 5x(1-x) - 8(x² -3)

= 3x²-6x - 5x + 5x² - 8x² +24 

= -11x +24

a) = (6x+1)² -2(6x+1)(6x-1)+(6x-1)²=(6x+1-6x+1)²=2²=4