Factor completely. 27x^(6)-3x^(2) Answer:

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms 27x^6 and 3x^2. The GCF of 27 and 3 is 3. The GCF of x^6 and x^2 is x^2. Therefore, the GCF of 27x^6 and 3x^2 is 3x^2.Factor out GCF: Factor out the GCF from the expression. The expression 27x^6 - 3x^2 can be written as 3x^2(9x^4 - 1).Recognize difference of squares: Recognize that 9x^4 - 1 is a difference of squares. 9x^4 is a perfect square, as (3x^2)^2 = 9x^4. 1 is a perfect square, as 1^2 = 1. The difference of squares can be factored as (a^2 - b^2) = (a + b)(a - b).Factor difference of squares: Factor the difference of squares. The expression 9x^4 - 1 can be factored as (3x^2 + 1)(3x^2 - 1).Combine GCF with factored form: Combine the GCF with the factored form of the difference of squares. The fully factored form of the expression is 3x^2(3x^2 + 1)(3x^2 - 1).

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Q. Factor completely.

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27 x^{6}-3 x^{2}

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Answer:

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms $27x^6$ and $3x^2$ . The GCF of $27$ and $3$ is $3$ . The GCF of $x^6$ and $x^2$ is $x^2$ . Therefore, the GCF of $27x^6$ and $3x^2$ is $3x^2$ .
Factor out GCF: Factor out the GCF from the expression. $\newline$ The expression $27x^6 - 3x^2$ can be written as $3x^2(9x^4 - 1)$ .
Recognize difference of squares: Recognize that $9x^4 - 1$ is a difference of squares. $\newline$ $9x^4$ is a perfect square, as $(3x^2)^2 = 9x^4$ . $\newline$ $1$ is a perfect square, as $1^2 = 1$ . $\newline$ The difference of squares can be factored as $(a^2 - b^2) = (a + b)(a - b)$ .
Factor difference of squares: Factor the difference of squares. $\newline$ The expression $9x^4 - 1$ can be factored as $(3x^2 + 1)(3x^2 - 1)$ .
Combine GCF with factored form: Combine the GCF with the factored form of the difference of squares. $\newline$ The fully factored form of the expression is $3x^2(3x^2 + 1)(3x^2 - 1)$ .