\(\left(\frac{1}{2}-\frac{1}{3}\right).6x+6x+2=67+64\)

\(\frac{\Rightarrow1}{6}.6x+6x+2=131\)

\(\Rightarrow x+6x=131-2\)

\(\Rightarrow7x=129\)

\(\Rightarrow x=\frac{129}{7}\)

8: =>6x^2-9x+2x-3-6x^2-12x=16

=>-19x=19

=>x=-1

`a)5y(2y-1)-(3y+2)(3-3y)`

`=10y^2-5y+(3y+2)(3y-3)`

`=10y^2-5y+9y^2-9y+6y-6`

`=19y^2-8y-6`

`b)(6x+1)^2-2(6x+1)(6x-1)+(6x-1)^2`

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

`=2^2=4`

`c)(2x+3)^2-2(2x+3)(x-20+(x-2)^2`

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

`=(x+5)^2`

`=x^2+10x+25`

\(a,=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-2b^3=6a^2b\\ b,=\left(6x+1-6x+1\right)^2=2^2=4\)

\(\text{a) }\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(6x+1\right)\left(6x-1\right)\\ =\left[\left(6x+1\right)-\left(6x-1\right)\right]^2\\ =\left[6x+1-6x+1\right]^2\\ =2^2\\ =4\)

\(\text{b) }3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^{16}-1\right)\left(2^{16}+1\right)\\ =2^{32}-1\)

\(1,\left(x-2\right)\left(x+2\right)\left(x^2+4\right)-\left(x^2-3\right)\left(x^2+3\right)\)

\(=\left(x^2-4\right)\left(x^2+4\right)-\left(x^2-9\right)\)

\(=x^2-16-x^2+9\)

\(=-7\)

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

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

\(=2^2=4\)

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

\(=4x^2+4x+1+4x^2-4x+1-2\left(x^2-6x+9\right)\)

\(=8x^2+2-2x^2+12x-18\)

\(=6x^2+12x-16\)

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

\(=x^2-2x+1-9x^2-12x-4\)

\(=-8x^2-14x-3\)

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

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

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

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

= (6x+1-6x+1)²

= 2²

=4

=[ (6x+1)-(6x-1) ]²