find the value of (-1) to the power n+(-1)to the power 2n+ (-1) to the power 2n+1 + (-1)to the power 4n+2 ​

Question

find the value of (-1) to the power n+(-1)to the power 2n+ (-1) to the power 2n+1 + (-1)to the power 4n+2

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Kylie 3 months 2021-10-15T15:50:23+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-15T15:51:54+00:00

    Answer:

    STEP

    1

    :

    Equation at the end of step 1

    (8 • (x6)) – 33×3

    STEP

    2

    :

    Equation at the end of step

    2

    :

    23×6 – 33×3

    STEP

    3

    :

    STEP

    4

    :

    Pulling out like terms

    4.1 Pull out like factors :

    8×6 – 27×3 = x3 • (8×3 – 27)

    Trying to factor as a Difference of Cubes:

    4.2 Factoring: 8×3 – 27

    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 : x3 is the cube of x1

    Factorization is :

    (2x – 3) • (4×2 + 6x + 9)

    Trying to factor by splitting the middle term

    4.3 Factoring 4×2 + 6x + 9

    The first term is, 4×2 its coefficient is 4 .

    The middle term is, +6x its coefficient is 6 .

    The last term, “the constant”, is +9

    Step-1 : Multiply the coefficient of the first term by the constant 4 • 9 = 36

    Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is 6 .

    -36 + -1 = -37

    -18 + -2 = -20

    -12 + -3 = -15

    -9 + -4 = -13

    -6 + -6 = -12

    -4 + -9 = -13

    For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

    Observation : No two such factors can be found !!

    Conclusion : Trinomial can not be factored

    Final result :

    x3 • (2x – 3) • (4×2 + 6x + 9)

    0
    2021-10-15T15:52:08+00:00

    Answer:

    hope it helps you…..

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