Simplify the expression: 2(x-1)(2x+2)^3[4(x-1)+(2x+2)]

[mansae]

\(\displaystyle 47.\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[4\, (x\, -\, 1)\, +\, (2x\, +\, 2)\right]\)

. . . . .\(\displaystyle =\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[4x\, -\, 4\, +\, 2x\, +\, 2\right]\)

. . . . .\(\displaystyle =\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[6x\, -\, 2\right]\)

. . . . .\(\displaystyle =\, 4\, (x\, -\, 1)\, (3x\, -\, 1)\, (2x\, +\, 2)^3\)

How did they go from the next to last line to the last?

how did 2(x-1)(2x+2)^3(6x-2) become 4(x-1)(3x-1)(2x+2)^3 ?

 

[Deleted member 4993]

\(\displaystyle 47.\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[4\, (x\, -\, 1)\, +\, (2x\, +\, 2)\right]\)

. . . . .\(\displaystyle =\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[4x\, -\, 4\, +\, 2x\, +\, 2\right]\)

. . . . .\(\displaystyle =\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[6x\, -\, 2\right]\)

. . . . .\(\displaystyle =\, 4\, (x\, -\, 1)\, (3x\, -\, 1)\, (2x\, +\, 2)^3\)

How did they go from the next to last line to the last?

how did 2(x-1)(2x+2)^3(6x-2) become 4(x-1)(3x-1)(2x+2)^3 ?

(6x-2) = 2 * ( 3x -1)

Then

2(x-1)(2x+2)^3(6x-2)

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

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

= 4(x-1)(3x-1)(2x+2)^3

 

[stapel]

\(\displaystyle 47.\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[4\, (x\, -\, 1)\, +\, (2x\, +\, 2)\right]\)

. . . . .\(\displaystyle =\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[4x\, -\, 4\, +\, 2x\, +\, 2\right]\)

. . . . .\(\displaystyle =\, 2\, (x\, -\, 1)\, (2x\, +\, 2)^3\, \left[6x\, -\, 2\right]\)

. . . . .\(\displaystyle =\, 4\, (x\, -\, 1)\, (3x\, -\, 1)\, (2x\, +\, 2)^3\)

how did 2(x-1)(2x+2)^3(6x-2) become 4(x-1)(3x-1)(2x+2)^3 ?

You can see that the x - 1 and the (2x + 2)³ are the same. What did you get when you looked at the 2 and the 6x - 2, and compared then with the 4 = 2*2 and the 3x - 1?

 

[mansae]

thanks guys, got it