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

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)