How do you factor completely #8x^3+1#?

Answer 1

Eva Adamson

Use the sum of cubes identity to find:

#8x^3+1 = (2x+1)(4x^2-2x+1)#

The sum of cubes identity can be written:

#a^3+b^3 = (a+b)(a^2-ab+b^2)#

Use this with #a=2x# and #b=1# as follows:

#8x^3+1#

#= (2x)^3+1^3#

#= (2x+1)((2x)^2-(2x)(1)+1^2)#

#= (2x+1)(4x^2-2x+1)#

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Answer 2

Eva Abramson

To factor completely the expression (8x^3 + 1), we can use the sum of cubes formula, which states that (a^3 + b^3 = (a + b)(a^2 - ab + b^2)). In this case, (8x^3) can be expressed as ((2x)^3) and (1) can be expressed as (1^3). Therefore, applying the sum of cubes formula, we get:

[8x^3 + 1 = (2x + 1)(4x^2 - 2x + 1).]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.