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Jan 20
To factorize 12x^2 - 27, we 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, a = √(12x^2) and b = √27.
First, let's simplify the expression inside the square roots:
√(12x^2) = √(4 * 3 * x^2) = 2x√3
√27 = √(9 * 3) = 3√3
Now, we can rewrite the expression as:
(2x√3 + 3√3)(2x√3 - 3√3)
Simplifying further, we get:
(2x + 3)(√3)(2x - 3)(√3)
Therefore, the factorization of 12x^2 - 27 is (2x + 3)(2x - 3)(√3)^2, or simply (2x + 3)(2x - 3)(3).
In this case, a = √(12x^2) and b = √27.
First, let's simplify the expression inside the square roots:
√(12x^2) = √(4 * 3 * x^2) = 2x√3
√27 = √(9 * 3) = 3√3
Now, we can rewrite the expression as:
(2x√3 + 3√3)(2x√3 - 3√3)
Simplifying further, we get:
(2x + 3)(√3)(2x - 3)(√3)
Therefore, the factorization of 12x^2 - 27 is (2x + 3)(2x - 3)(√3)^2, or simply (2x + 3)(2x - 3)(3).
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