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motikmotik
2 years ago
13

Use a special-product rule to factor the perfect-square trinomial. 81y^2+ 126y + 49

Mathematics
1 answer:
Ivahew [28]2 years ago
7 0

Answer:

The perfect -square trinomial

                  (9y+7)²

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given polynomial equation

                        81 y² + 126 y +49

               ⇒     9² y² + 2(9)(7)y + 7²

                ⇒   (9y)² + 2(9)(7)y +7²

we will use formula

   (a+b)² = a² + 2ab +b²

             ⇒ (9y+7)²

<u><em>Final answer:-</em></u>

The perfect -square trinomial

                  (9y+7)²

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Find the product. Simplify your answer.<br> -5 • 9t<br> 7s 7
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Answer:

-13            

 ——— = -0.20635  

 63            

Step-by-step explanation:

Step  1  :

           7

Simplify   —

           9

Equation at the end of step  1  :

 4    7

 — -  —

 7    9

Step  2  :

           4

Simplify   —

           7

Equation at the end of step  2  :

 4    7

 — -  —

 7    9

Step  3  :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       7  

     The right denominator is :       9  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

7 1 0 1

3 0 2 2

Product of all  

Prime Factors  7 9 63

     Least Common Multiple:

     63  

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 9

  Right_M = L.C.M / R_Deno = 7

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      4 • 9

  ——————————————————  =   —————

        L.C.M              63  

  R. Mult. • R. Num.      7 • 7

  ——————————————————  =   —————

        L.C.M              63  

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

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———————————————  =  ———

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Final result :

 -13            

 ——— = -0.20635  

 63            

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