1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
puteri [66]
3 years ago
11

15 points for 1 question??

Mathematics
1 answer:
mestny [16]3 years ago
5 0

Answer:a7b2-ab2  

Final result :

 ab2•(a+1)•(a2-a+1)•(a-1)•(a2+a+1)

Step by step solution :

Step  1  :

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  a7b2 - ab2  =   ab2 • (a6 - 1)  

Trying to factor as a Difference of Squares :

2.2      Factoring:  a6 - 1  

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 : 1 is the square of 1

Check :  a6  is the square of  a3  

Factorization is :       (a3 + 1)  •  (a3 - 1)  

Trying to factor as a Sum of Cubes :

2.3      Factoring:  a3 + 1  

Theory : A sum of two perfect cubes,  a3 + b3 can be factored into  :

            (a+b) • (a2-ab+b2)

Proof  : (a+b) • (a2-ab+b2) =

   a3-a2b+ab2+ba2-b2a+b3 =

   a3+(a2b-ba2)+(ab2-b2a)+b3=

   a3+0+0+b3=

   a3+b3

Check :  1  is the cube of   1  

Check :  a3 is the cube of   a1

Factorization is :

            (a + 1)  •  (a2 - a + 1)  

Trying to factor by splitting the middle term

2.4     Factoring  a2 - a + 1  

The first term is,  a2  its coefficient is  1 .

The middle term is,  -a  its coefficient is  -1 .

The last term, "the constant", is  +1  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 1 = 1  

Step-2 : Find two factors of  1  whose sum equals the coefficient of the middle term, which is   -1 .

     -1    +    -1    =    -2  

     1    +    1    =    2  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Trying to factor as a Difference of Cubes:

2.5      Factoring:  a3-1  

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check :  1  is the cube of   1  

Check :  a3 is the cube of   a1

Factorization is :

            (a - 1)  •  (a2 + a + 1)  

Trying to factor by splitting the middle term

2.6     Factoring  a2 + a + 1  

The first term is,  a2  its coefficient is  1 .

The middle term is,  +a  its coefficient is  1 .

The last term, "the constant", is  +1  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 1 = 1  

Step-2 : Find two factors of  1  whose sum equals the coefficient of the middle term, which is   1 .

     -1    +    -1    =    -2  

     1    +    1    =    2  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 ab2•(a+1)•(a2-a+1)•(a-1)•(a2+a+1)

Step-by-step explanation:

You might be interested in
A point with coordinates (a, b) is plotted on a coordinated plane. The values of a and b can be any positive or negative integer
Diano4ka-milaya [45]

Answer:

Any negative and positive number can be your coordinates.

Step-by-step explanation:

As long as you don't have any restrictions as to what the coordinates can be, you're good to go!

Hope this helps!

8 0
3 years ago
In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G). A quality control
lianna [129]

Answer:

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

Step-by-step explanation:

There are a total of <em>N</em> = 25 aluminum castings.

Of these 25 aluminum castings, <em>n</em>₁ = 4 castings are defective (D) and <em>n</em>₂ = 21 are good (G).

It is provided that a quality control inspector randomly selects three of the twenty-five castings without replacement to test.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!(n-k)!}

Compute the number of samples that are possible as follows:

{25\choose 3}=\frac{25!}{3!\times (25-3)!}

      =\frac{25\times 24\times 23\times 22!}{3!\times 22!}\\\\=\frac{25\times 24\times 23}{3\times 2\times 1}\\\\=2300

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

6 0
3 years ago
Determine if the following system of equations has no solutions, infinitely many
mylen [45]
This are similar answers to your questions.

8 0
2 years ago
PLEASEE HELPP MEEEE!!!!!!!!! PLEASEE!!!!!!!!!!!!!!!<br><br> what is the value of x?
andreev551 [17]
..........................
3 0
3 years ago
Please help! I'll mark as brainliest
Rudik [331]

Answer:

your work is not clearly taking sorry i can't see

7 0
2 years ago
Other questions:
  • Which is more 3/8 or 3/6
    8·1 answer
  • Plz help meeeee I'm confused
    11·1 answer
  • Simplify the expression. 7 √x • 7 √x • 7 √x
    14·1 answer
  • HELP ASAP!! Someone please help me solve #19 with steps on how to solve?
    7·1 answer
  • Andrea tiene 40 dulces y los reparte entre sus seis amigos Cuántos dulces Le tocará a cada uno​
    5·2 answers
  • What is the approximate line of best fit for the scatter plot
    15·1 answer
  • In a class of 300 students ,20% are girls how many boys are there?
    8·2 answers
  • Volume is expressed in
    8·1 answer
  • I don’t understand the question and I can’t find anything in my notes to help
    10·1 answer
  • The points (-3, -3) and (5, r) lie on a line with slope 3/2<br> Find the missing coordinate r.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!