Question

Разложите на множители: 3x^4-243 A) 3(x-9)^2 B) 3(x^2-9)^2 C) 3(x-3)(x+3)(x^2+9) D) (3x^2-9)(3x^2+9) E) 3(x^4-240)​

Answer 1

Ответ:

C) 3(x-3)(x+3)(x²+9)..

Answer 2

Alright, let's factorize the expression $3x^4 - 243$. First, notice that $243$ can be expressed as $3^5$. So, we can rewrite the expression as:

$3x^4 - 243 = 3x^4 - 3^5$

Now, we can use the difference of cubes formula, which is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. In this case, let $a = x^2$ and $b = 3$:

$3x^4 - 3^5 = 3(x^2)^2 - 3^5$

Now apply the difference of cubes formula:

$= 3(x^2 - 3)(x^2 + 3x^2 + 3^2)$

Simplify further:

$= 3(x^2 - 3)(4x^2 + 9)$

So, the correct answer is option D) $(3x^2 - 9)(4x^2 + 9)$.