Question Write the following expression as a simplified polynomial in standard form $$ 3(x+4)^{2}+2(x+4)+4 $$

Question

UpStudy AI · Accepted Answer

First, we'll expand the square term:
  (x + 4)² = x² + 8x + 16.

Multiply by 3:
  3(x² + 8x + 16) = 3x² + 24x + 48.

Now, expand the middle term:
  2(x + 4) = 2x + 8.

Finally, add all terms together with the constant 4:
  3x² + 24x + 48 + 2x + 8 + 4.

Combine like terms:
  x² terms: 3x².
  x terms: 24x + 2x = 26x.
  Constant terms: 48 + 8 + 4 = 60.

The simplified polynomial in standard form is:
  3x² + 26x + 60.
The simplified polynomial in standard form is $$ 3x^2 + 26x + 60 $$.

Question Write the following expression as a simplified polynomial in standard form \[ 3(x+4)^{2}+2(x+4)+4 \]