Factor:
125x^3 - 27 = 0
There's a rule for factoring this type of polynomial:
x^3 - a^3 = (x-a)(x^2 + ax + a^2)
Can you take it from here??
To factor the given expression, we can first notice that it follows a special form called the difference of cubes. The difference of cubes formula states that:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
In our case, a is 5x, and b is 3. Plugging these values into the formula, we get:
(5x)^3 - 3^3 = (5x - 3)((5x)^2 + (5x)(3) + 3^2)
Simplifying further:
125x^3 - 27 = (5x - 3)(25x^2 + 15x + 9)
Therefore, the factored form of the expression 125x^3 - 27 = 0 is (5x - 3)(25x^2 + 15x + 9) = 0.