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sdas [7]
3 years ago
14

(x 4 - 81) (x - 3) . write answers in descending power of x. (division)

Mathematics
1 answer:
Zinaida [17]3 years ago
4 0

Answer:

  x^3+3x^2+9x+27

Step-by-step explanation:

\dfrac{x^4-81}{x-3}=\dfrac{(x^2-9)(x^2+9)}{x-3}=\dfrac{(x-3)(x+3)(x^2+9)}{(x-3)}\\\\=(x+3)(x^2+9)=x^3+3x^2+9x+27

_____

The factoring of the difference of squares is used (twice):

  a² -b² = (a -b)(a +b)

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What is the factorise 3m-6
cupoosta [38]

The answer is:      "  3(m − 2)  "  .

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  →  The "factorized version" of the binomial expression, " 3m − 6 " ,  is:

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                →   "  3(m − 2) " .

__________________________________

Explanation:

To solve:

__________________________________

<u>Note</u>:  We are given the expression:  " 3m − 6 " ;

and we are asked to "factorize" this expression.

Note that this expression is a "binomial expression" — which means there are two (2) terms — in this case:   "3m" and "6" .

Since only one (1) of these 2 (two) terms has a variable, and the remaining terms is a "constant" (non-zero integer), write these 2 (two) terms as:

 1)  the coefficient of the variable given in the term shown with a "coefficient" :

       →   that is:  "3"  ;  and:

 2)  the other term:  "6" .

→  With the numbers:  "3 and 6" , we can factor out a "3" ;  

          →  {since:  " 6 ÷ 3 = 2 "} ;

 →   So;  given:  

               " 3m − 6 " ;  

 →   We can "factor out" a "3" ; as follows:

           →   Take the first term:  " 3m " :

                    " 3m  =  3 * m " ;

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           →   Take the second term:  "  6 " :

                    "  6 = 3 * (what value?) ;

                 → divide each of this equation by "3" ;

    to isolate the "missing value" on one side of the equation; & to solve for the "missing value" ; as follows:

        →           "  6 / 3 = [ 3 * (what value?) ] / 3  ;

                    →  to get:  " 2  =  "(the missing value)"  ;

    →   So;    "  6 = 3 * (what value?) ;

           →     " 6 = 3 * 2 " .  

           →   Take the second term:  "  6 " :

           →     " 6 = 3 * 2 " .

__________________________________

So:    " 3m − 6 "  =  (3 * m) − (3 * 2) " .  

Factor out a "3" ;  as follows:

__________________________________

    →  " 3m − 6 "  =  (3 * m) − (3 * 2) " ;

                           =   " 3(m − 2)  "

__________________________________

Let us check our answer:

__________________________________

Note the "distributive property of multiplication"  :

__________________________________

        a(b + c) = ab +  ac ;  

        a(b − c) = ab −  ac ;

__________________________________

So:  Take our answer:  " 3(m − 2) " .

__________________________________

" 3(m − 2)  = ?  (3*m)  −  (3*2)  " ??  ;

__________________________________

Let us substitute "4" for "m" ;  in both sides of the equation;

              →  to see if the equation holds true;  i.e. to see if both sides of the equation are equal when:  " m = 4 " ;

__________________________________

 We have:

__________________________________

     →  " 3(m − 2)  = ?  (3*m)  −  (3*2)  " ??  ;

First let us rewrite this equation;  substitute "4" for "m" ; as follows:

     →   " 3(4 − 2)  = ?  (3*4)  −  (3*2)  " ??  ;

__________________________________

And calculate;  to see if each side of the equation is equal ; i.e. to see if the equation holds true; as follows:

     →   " 3(2)  = ?  (12)  −  (6)  " ??  ;

     →   "  6  = ?  (6)  " ??  ;

     →   "  6 = 6 " !  Yes!  The equation holds true!

__________________________________

Hope this answer was helpful!

Best wishes!

__________________________________

8 0
3 years ago
If a=3, b=5, and c=2, what is a²c²+2(b+c)÷b
finlep [7]
38.8 is the answer. Using pemdas you should find work leading to that
4 0
3 years ago
(1) 8/5+0=8/5=0+8/5 <br>(2) (3/5+1/2)=2(3/5)+2(1/2)​
Bond [772]

Answer:

(1)communicative property

(2) i d k

Step-by-step explanation:

7 0
3 years ago
Patrice, by himself, can paint four rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours.
Elodia [21]

-- The whole discussion involves 4 rooms, never more and never less,
so we can call the 4 rooms "1 job" for simplicity.

-- Patrice, by himself, does the job in 10 hours.  So he does 1/10 of
the job each hour.

-- Working together, Patrice and April do the job in 6 hours.  So when
they work together, they do 1/6 of the job each hour.

-- April's part of the job is (1/6 - 1/10) = (5/30 - 3/30) = 2/30 = 1/15 job per hour.

-- Her unit rate alone is  1/15 job per hour, or  <em>15 hours</em> per job.


5 0
2 years ago
Hello i need help with this plz
gayaneshka [121]

Answer: Sorry i only could so #3

32/30

Step-by-step explanation:

7 0
2 years ago
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