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1 July, 06:59

Which of the following is the correct factorization of the polynomial below?

8x3 + 27y3

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Answers (1)
  1. 1 July, 07:09
    0
    (2x + 3y) • (4x2 - 6xy + 9y2)

    Step-by-step explanation:

    Step 1:

    Equation at the end of step 1:

    (8 • (x3)) + 33y3

    Step 2:

    Equation at the end of step 2:

    23x3 + 33y3

    Step 3:

    Trying to factor as a Sum of Cubes:

    3.1 Factoring: 8x3+27y3

    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 : 8 is the cube of 2

    Check : 27 is the cube of 3

    Check : x3 is the cube of x1

    Check : y3 is the cube of y1

    Factorization is:

    (2x + 3y) • (4x2 - 6xy + 9y2)
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