Question

What is the result when we simplify the expression ( 1 + 1 x ) ( 1 − 2 x + 1 ) ( 1 + 2 x − 1 ) ( 1 + 1 x ) ( 1 − 2 x + 1 ) ( 1 + 2 x − 1 ) ?

Answer 1

Answer:

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

Step-by-step explanation:

$\left(1+1\cdot \:x\right)\left(1-2x+1\right)\left(1+2x-1\right)\left(1+1\cdot \:x\right)\left(1-2x+1\right)\left(1+2x-1\right)$

$=\left(1+1\cdot \:x\right)\left(1+2x-1\right)\left(1+1\cdot \:x\right)\left(1-2x+1\right)^{1+1}\left(1+2x-1\right)$

$=\left(1+2x-1\right)\left(1+1\cdot \:x\right)^{1+1}\left(1-2x+1\right)^2\left(1+2x-1\right)$

$=\left(1+2x-1\right)\left(1+1\cdot \:x\right)^{1+1}\left(1-2x+1\right)^2\left(1+2x-1\right)$

$=\left(1+2x-1\right)\left(1+1\cdot \:x\right)^2\left(1-2x+1\right)^2\left(1+2x-1\right)$

$=\left(1+1\cdot \:x\right)^2\left(1-2x+1\right)^2\left(1+2x-1\right)^{1+1}$

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

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

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

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

Hope I helped you!

Success!