I need to factor = 16s^6-2f^6
My answer is 2(s-8)
what happened to the f^6 ?
(If you expanded your answer would you get the original ?)
16s^6-2f^6
= 2(8s^6 - f^6)
now 8s^6 = (2s^2)^3 and f^6 = (f^2)^3 so
knowing that A^3 - B^3 = (A-B)(a^2 + AB + b^2)
2(8s^6 - f^6)
= 2(2s^2 - f^2)(4s^4 + 2s^2f^2 + f^4)
How can 2s - 16 be the same as 16s^6-2f^6 ? Those functions are totally different. One is sixth order in s and is linear in s. One has f as a variable and the other does not.
16s^6 -2f^6 = 2(8s^6 - f^6)
= 2*(sqrt8 s^3 -f^3)(sqrt8 s^3+ f^3)
Further factoring of the cubic terms is possible. Look up how to factor a^3 - b^3 and a^3 + b^3.
thank u
To factor the expression 16s^6 - 2f^6, we can first look for a common factor. In this case, both terms have a factor of 2.
Step 1: Factor out the common factor of 2:
2(8s^6 - f^6)
Next, we can observe that 8s^6 - f^6 is a difference of squares, which can be factored using the formula: a^2 - b^2 = (a + b)(a - b).
In this case, a = 2s^3 and b = f^3. So, we can replace a and b in the formula:
2(2s^3 + f^3)(2s^3 - f^3)
Finally, we can further simplify the expression in the parentheses by factoring the difference of cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Using this formula, we can factor 2s^3 - f^3:
2(2s^3 + f^3)((2s^3)^2 + (2s^3)(f^3) + (f^3)^2)
Simplifying further, we get:
2(2s^3 + f^3)(4s^6 + 4s^3f^3 + f^6)
And that is the fully factored form of 16s^6 - 2f^6.
So, your answer of 2(s-8) is incorrect. The correct factored form is 2(2s^3 + f^3)(4s^6 + 4s^3f^3 + f^6).