Simplify the expression:

\[ 2((x+1)^3 - (x+1)^2 + (x+1)) + 3 \]

( x + 1 )^3 = x^3 + 3x^2 +3x + 1; (x + 1 )^2 = x^2 + 2x + 1; => (2((x+1) ^3 – (x+1) ^2 + (x+1)) )+3 =2( x^3 + 3x^2 +3x + 1 - x^2 -2x - 1 + x + 1 ) + 3 = 2( x^3 + 2x^2 + 2x + 1 ) + 3 = = 2x^3 +4x^2 +4x + 5.

Answered by crisforp | 2024-06-10

The expression simplifies to 2 x 3 + 4 x 2 + 4 x + 5 . This is achieved by expanding the cubes and squares, combining like terms, and performing the multiplications. The final result is presented in a simplified polynomial form.
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Answered by crisforp | 2024-12-26