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How do you factor #9b^4-16c^4#?

Answer 1

Nathan Axel

Recognize that this is a difference of squares, which factor as follows:

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

In your scenario:

#9b^4-16c^4#

#=>(3b^2)^2-(4c^2)^2=(3b^2+4c^2)(3b^2-4c^2)#

Note that this is a fine final answer, but that #3b^2-4c^2# can also be treated as a difference of squares.

#3b^2-4c^2#

#=>(bsqrt3)^2-(2c)^2=(bsqrt3+2c)(bsqrt3-2c)#

So,

#9b^4-16c^4=(3b^2+4c^2)(bsqrt3+2c)(bsqrt3-2c)#

#9b^4-16c^4=(3b^2+4c^2)(3b^2-4c^2)#

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Answer 2

Avery Alexander

To factor the expression (9b^4 - 16c^4), you can use the difference of squares formula, which states that (a^2 - b^2 = (a + b)(a - b)). Applying this formula, the expression factors to ((3b^2 + 4c^2)(3b^2 - 4c^2)).

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Answer 3

Eva Abramson

To factor the expression 9b^4 - 16c^4, you can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b). In this case:

9b^4 - 16c^4 = (3b^2)^2 - (4c^2)^2

Using the difference of squares formula:

= (3b^2 + 4c^2)(3b^2 - 4c^2)

Therefore, the factored form of 9b^4 - 16c^4 is (3b^2 + 4c^2)(3b^2 - 4c^2).

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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.