19x^2+7-[3(x^2-7)+9]
how do you simplify

 19x2+6-(3(x2-7)+9) Final result : 2 • (8x2 + 9) Step by step solution :Step  1  :Trying to factor as a Difference of Squares :

 1.1      Factoring:  x2-7 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 7 is not a square !! 

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  1  : ((19•(x2))+6)-(3•(x2-7)+9) Step  2  :Equation at the end of step  2  : (19x2 + 6) - (3x2 - 12) Step  3  :Step  4  :Pulling out like terms :

 4.1     Pull out like factors :

   16x2 + 18  =   2 • (8x2 + 9) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 8x2 + 9
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q  then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  8  and the Trailing Constant is  9. 

 The factor(s) are: 

of the Leading Coefficient :  1,2 ,4 ,8 
 of the Trailing Constant :  1 ,3 ,9 

 Let us test

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      17.00        -1     2      -0.50      11.00        -1     4      -0.25      9.50        -1     8      -0.13      9.13        -3     1      -3.00      81.00   

Note - For tidiness, printing of 19 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result : 2 • (8x2 + 9)

Pemdas = Parenthesis, exponents, multiply, divide, addition, subtract. So first you need to break it down and solve all in parenthesis by distributing the 3, so 3*x^2 = 3x^2 & 3*-7= -21. NEW equation would be 19x^2+7-[3x^2-21+9]. Now you're going to distribute that negative sign and combine like terms. 19x^2 -3x^2 is now 16x^2. 7-(-21)+9 solve for that which is 7+21 = 28 then add the 9 which will now be 37. so the simplify answer is now 16x^2 + 28

1856 is the answer because
1852+ 4 is 1856