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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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