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44 - ( 9x² + 36 x + 36 ) = 8 - 36 x - 9 x²

The result is: 44 - (3x+6)^2 = - 9x^2 - 36x + 8 when simplified

44 - (3x + 6)²

i.e. 44 - (9x² + 36x + 36)

=> 44 - 9x² - 36x - 36

so, - 9x² - 36x + 8

:)>

Written as a simplified polynomial in standard form, what is the result when (3x+6)² is subtracted from 4

(3x+6)² = 9x² + 36x + 36

4 - (9x² + 36x + 36) =

-9x² - 36x - 32..................ANS

44 - (9x^2 + 36x + 36)

= -(9x^2 + 36x - 8)

Method 1

44 - (3x+6)² = 44 - (9x² + 36x + 36)            ← (a+b)² = a² + 2ab + b²

                    = 44 - 9x² - 36x - 36

                    = -9x² - 36x + 8                       ← ax² + bx + c

                                                              standard polynomial form

Method 2

44 - (3x+6)² = 44 - (3x+6)(3x+6)

                    = 44 - [(3x+6)(3x+6)]                       ← Now, FOIL what's inside the brackets

                    = 44 - [3x*3x + 3x*6 + 6*3x + 6*6]

                    = 44 - [9x² + 18x + 18x + 36]

                    = 44 - [9x² + 36x + 36]                      ← Now, distribute the minus sign

                    = 44 - 9x² - 36x - 36                          ← Now, collect like terms

                    = -9x² - 36x - 36 + 44

                    = -9x² - 36x + 8                                  ← ax² + bx + c

                                                                         standard polynomial form