Question
Factor completely.
2x^4-32
2x^4-32
Answers
Answered by
GPT 3.5
To factor the expression 2x^4 - 32, we can first factor out the greatest common factor (GCF), which is 2:
2(x^4 - 16)
Next, we can rewrite the expression inside the parentheses as the difference of two squares:
2((x^2)^2 - 4^2)
Using the identity a^2 - b^2 = (a + b)(a - b), we can further factor:
2((x^2 + 4)(x^2 - 4))
Since x^2 - 4 is also a difference of squares, we can factor it again:
2((x^2 + 4)(x + 2)(x - 2))
Therefore, the completely factored form of 2x^4 - 32 is 2(x^2 + 4)(x + 2)(x - 2).
2(x^4 - 16)
Next, we can rewrite the expression inside the parentheses as the difference of two squares:
2((x^2)^2 - 4^2)
Using the identity a^2 - b^2 = (a + b)(a - b), we can further factor:
2((x^2 + 4)(x^2 - 4))
Since x^2 - 4 is also a difference of squares, we can factor it again:
2((x^2 + 4)(x + 2)(x - 2))
Therefore, the completely factored form of 2x^4 - 32 is 2(x^2 + 4)(x + 2)(x - 2).