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