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valina [46]
3 years ago
9

What is the factored form of 8x^24-27y^6

Mathematics
2 answers:
pochemuha3 years ago
7 0
<span>
</span>



<span> <span> <span> <span> </span> <span>
</span></span></span></span> <span><span> 8x24-27y6</span> </span>Final result :<span> (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4) </span>

Step by step solution :<span> Step  1  :</span>Skip Ad
<span>Equation at the end of step  1  :</span><span><span> (8 • (x24)) - 33y6 </span><span> Step  2  :</span></span><span>Equation at the end of step  2  :</span><span> 23x24 - 33y6 </span><span> Step  3  :</span>Trying to factor as a Difference of Squares :

<span> 3.1 </span>     Factoring: <span> 8x24-27y6</span> 

Theory : A difference of two perfect squares, <span> A2 - B2  </span>can be factored into <span> (A+B) • (A-B)

</span>Proof :<span>  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 =
        <span> A2 - B2</span>

</span>Note : <span> AB = BA </span>is the commutative property of multiplication.

Note : <span> - AB + AB </span> equals zero and is therefore eliminated from the expression.

Check :<span>  8  is not a square !!

</span>Ruling : Binomial can not be factored as the
difference of two perfect squares

Trying to factor as a Difference of Cubes:

<span> 3.2 </span>     Factoring: <span> 8x24-27y6</span> 

Theory : A difference of two perfect cubes, <span> <span>a3</span> - <span>b3</span> </span> can be factored into
            <span>  (a-b) • (a2 +ab +b2)</span>

Proof : <span> (a-b)•(a2+ab+b2) =
            <span>a3</span>+<span>a2b</span>+<span>ab2</span>-<span>ba2</span>-<span>b2a</span>-<span>b3</span> =
            <span>a3</span>+(<span>a2b</span>-<span>ba2</span>)+(<span>ab2</span>-<span>b2a</span>)-<span>b3</span> =
            <span>a3</span>+0+0+<span>b3</span> =
            <span>a3</span>+<span>b3</span></span>

Check :  8  is the cube of  2 

Check :  27  is the cube of   3 
Check :<span>  x24</span> is the cube of <span>  x8</span>

Check :<span>  y6</span> is the cube of <span>  y2</span>

<span>Factorization is :
</span>            <span> <span>(2x8 - 3y2)</span>  • </span><span> (4x16 + 6x8y2 + 9y4)</span> 

Trying to factor as a Difference of Squares :

<span> 3.3 </span>     Factoring: <span> 2x8 - 3y2</span> 

Check :<span>  2  is not a square !!

</span>Ruling : Binomial can not be factored as the
difference of two perfect squares

Trying to factor a multi variable polynomial :

<span> 3.4 </span>   Factoring   <span> 4x16 + 6x8y2 + 9y4</span> 

Try to factor this multi-variable trinomial using trial and error<span> 

 </span>Factorization fails

Final result :<span> (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4) </span>
Nana76 [90]3 years ago
6 0
The answer will be (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
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if 7 &lt; 5, then 5 &lt; 3 state the inverse, contrapositive, and converse of each conditional statement. then indicate whether
RUDIKE [14]

The given conditional statement is : If 7<5, then 5<3.

Inverse: If 7≥5 then 5≥3 (The inverse is true)

Contrapositive: if 5≥3 then 7≥5 (The contrapositive is true)

Converse: if 5<3 then 7<5 (The converse is true)

From the properties of conditional statement we know that:

if p→q then

  • inverse is : \backsim p \rightarrow \backsim q
  • contrapositive:\backsim q \rightarrow \backsim p
  • Converse:q \rightarrow p

Let us elaborate on the above conditions. Let us take two statement p and q  such that If p happens then q also happens.

  • The inverse of a conditional statement is given as "if not p then not q"the converse is given as "if q then p"The contrapositive of the statement states "if not q then not p"
  • The following statements can be used for converting the conditional statements to its inverse, converse or contrapositive.

To learn more about conditional statements:

brainly.com/question/7066208

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3 0
1 year ago
A store sells peanuts by the pound. Jerry paid 4.59 for 5.4 pounds of peanuts. At that rate, how much would he pay for 7.8 pound
nikdorinn [45]
If $4.59 = 5.4 peanuts
         $x = 7. 8 peanuts

Cross multiply and you get:

5.4x = (4.59)(7.8)
      x = ((4.59)(7.8)) / 5.4
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6 0
3 years ago
A bus ride for a senior citizen cost $1.25. A monthly pass costs $35.
Bond [772]

Answer:

25 or more

Step-by-step explanation:

30/1.is 24 so it would be 25 or more times for it to be a better deal

7 0
3 years ago
Solve the equation 5x + 2(2x -23) = -154
Anon25 [30]

\boxed{\large{\bold{\blue{ANSWER~:) }}}}

  • 5x+2(2x-23)=-154

  • 5x+4x-46=-154

  • 9x-46=-154

  • 9x=-154+46

  • 9x=-108

  • x=\sf{\dfrac{-108}{9}  }

  • x=-12
4 0
3 years ago
Read 2 more answers
I need this assignment done will give brainliest and extra points.
Travka [436]

Answer:

1a.2.5x³-2.25x²+3.5x-1.5

1b.No, they aren't equal. (worked out the product for both and they weren't equal, see below)

2a.-2x⁶+7x⁴+3x³-3x²+11x+20

2b.Yes. When multiplying, it doesn't matter which term/expression you put first

3. The equation has two solutions: x=-2, x=3

Step-by-step explanation:

1. (a)

(0.5x-0.25)(5x²-2x+6)

0.5x(5x²-2x+6)-0.25(5x²-2x+6)

2.5x³-x²+3x -1.25x²+0.5x-1.5

2.5x³-2.25x²+3.5x-1.5

(b)

(0.25x-0.5)(5x²-2x+6)

0.25x(5x²-2x+6)-0.5(5x²-2x+6)

1.25x³-0.5x²+1.5x -2.5x²+x-3

1.25x³-3x²+2.5x-3

This is not equal to our answer for 1(a), so we can see they're not the same.

2(a)

(-2x³+x-5)(x³-3x-4)

-2x³(x³-3x-4) +x(x³-3x-4) -5(x³-3x-4)

-2x⁶+6x⁴+8x³ +x⁴-3x²-4x -5x³+15x+20

-2x⁶+7x⁴+3x³-3x²+11x+20

(b)

Yes. When multiplying, it doesn't matter which term/expression you put first: xy=yx. For example, 2(3)=6 and 3(2)=6.

3

2x²-2x-12=0

(divide each term by 2)

x²-x-6=0

(x+2)(x-3)=0

Anything multiplies by zero is zero, so either x+2=0 or x-3=0

If x+2=0, x=-2. If x-3=0, x=3.

The equation has two solutions: x=-2, x=3

8 0
3 years ago
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