How do I factor b^3(a^3b^3 - 1)?
The b^3 is already factored out. For the term in parentheses, make use of the fact that
x^3 -1 = (x - 1)(x^2 + x + 1)
and substitute ab for x.
so is this the answer?
No. It will be the answer when you combine the steps as I described.
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-5x-y=21
To factor the expression b^3(a^3b^3 - 1), we can first identify that the expression inside the parentheses, (a^3b^3 - 1), is in the form of a difference of cubes.
The difference of cubes formula is given by:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
In our case, a^3b^3 - 1 can be recognized as (a^3)^1(b^3)^1 - 1^1.
So we can rewrite the expression as follows:
b^3(a^3b^3 - 1) = b^3[(a^3)^1(b^3)^1 - 1^1]
Now, applying the difference of cubes formula, we have:
b^3(a^3b^3 - 1) = b^3[(a^3)(b^3) - 1] = b^3(a^3b^3 - 1^3) = b^3(a^3b^3 - 1^3)
Finally, we can conclude that the expression b^3(a^3b^3 - 1) is equal to b^3 multiplied by the binomial (a^3b^3 - 1^3), which is typically written as b^3(a^3b^3 - 1).