Mathematics, 25.11.2019 23:31 hannahelisabeth19

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

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8x24-27y6 Final result : (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4) Step by step solution : Step 1 :Skip Ad
Equation at the end of step 1 : (8 • (x24)) - 33y6 Step 2 :Equation at the end of step 2 : 23x24 - 33y6 Step 3 :Trying to factor as a Difference of Squares :

3.1      Factoring: 8x24-27y6

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 : 8 is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Trying to factor as a Difference of Cubes:

3.2      Factoring: 8x24-27y6

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 : 8 is the cube of 2

Check :  27  is the cube of   3
Check : x24 is the cube of x8

Check : y6 is the cube of y2

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

Trying to factor as a Difference of Squares :

3.3 Factoring: 2x8 - 3y2

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Trying to factor a multi variable polynomial :

3.4 Factoring 4x16 + 6x8y2 + 9y4

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

Factorization fails

Final result : (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)

Answer from: Quest

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation:

Answer from: Quest

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