Complete the statement below.
( ) (12x + 19y) = 144x^2 (x to the 2nd power) - 361y^2 (y to the 2nd power)

Step-by-step explanation:

(12x - 19y) (12x + 19y) = 144x^2-361y^2

Maybe 12 x

Step-by-step explanation: first step Factor 144 into its prime factors

          144 = 24 • 32

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          144 = 24 • 32

No factors remain inside the root !!

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          12 = 22 • 3

At the end of this step the partly simplified SQRT looks like this:

        12 sqrt(x2) step 2 1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x8)=x4

    (3.2) sqrt(x-6)=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x2•sqrt(x)

    (4.2) sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

     SQRT(x2) = x then you Combine both simplifications sqrt (144x2) =

       12 x

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

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step-by-step explanation:

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