Question

Factorise 1-16x^2+64x^4

Answer 1

Step-by-step explanation:

Step by Step Solution:

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x4" was replaced by "x^4". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(1 - (16 • (x2))) + 26x4

STEP

2

:

Equation at the end of step

2

:

(1 - 24x2) + 26x4

STEP

3

:

Trying to factor by splitting the middle term

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Answer 2

Answer:

Step by Step Solution:

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x4" was replaced by "x^4". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(1 - (16 • (x2))) + 26x4

STEP

2

:

Equation at the end of step

2

:

(1 - 24x2) + 26x4

STEP

3

:

Trying to factor by splitting the middle term

3.1 Factoring 64x4-16x2+1

The first term is, 64x4 its coefficient is 64 .

The middle term is, -16x2 its coefficient is -16 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 64 • 1 = 64

Step-2 : Find two factors of 64 whose sum equals the coefficient of the middle term, which is -16 .

-64 + -1 = -65

-32 + -2 = -34

-16 + -4 = -20

-8 + -8 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -8

64x4 - 8x2 - 8x2 - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

8x2 • (8x2-1)

Add up the last 2 terms, pulling out common factors :

1 • (8x2-1)

Step-5 : Add up the four terms of step 4 :

(8x2-1) • (8x2-1)

Which is the desired factorization