Respuesta :
Answer:
see explanation
Step-by-step explanation:
This is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
16[tex]x^{8}[/tex] = ( 4[tex]x^{4}[/tex] )² ⇒ a = 4[tex]x^{4}[/tex]
1 = 1² ⇒ b = 1
Hence
16[tex]x^{8}[/tex] - 1
= (4[tex]x^{4}[/tex] )² - 1²
= (4[tex]x^{4}[/tex] - 1)(4[tex]x^{4}[/tex] + 1)
4[tex]x^{4}[/tex] - 1 ← is also a difference of squares and factors as
(2x² - 1)(2x² + 1)
Thus
16[tex]x^{8}[/tex] - 1
= (2x² - 1)(2x² + 1)(4[tex]x^{4}[/tex] + 1 )
The factor of 16x⁸ − 1 is (2x² - 1)(2x² + 1)(4x⁴ + 1 ) after applying the identity.
What is an expression?
It is defined as the combination of constants and variables with mathematical operators.
We have:
[tex]= \rm 16x^8 -1[/tex]
From the identity:
[tex]\rm a^2-b^2=\left(a+b\right)\left(a-b\right)[/tex]
[tex]= \rm (4x^4)^2 -1[/tex]
[tex]\rm = (4x^4 - 1)(4x^4 + 1)[/tex]
Again applying identity in first term
= (2x² - 1)(2x² + 1)(4 + 1 )
Thus, the factor of 16x⁸ − 1 is (2x² - 1)(2x² + 1)(4 + 1 ) after applying the identity.
Learn more about the expression here:
brainly.com/question/14083225
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