Respuesta :
Given:
The given expression is [tex]16 x^{8}-1[/tex]
We need to determine the factor of the given expression.
Factor:
Let us rewrite the given expression.
Thus, we have;
[tex]\left(4 x^{4}\right)^{2}-1^{2}[/tex]
Since, the above expression is of the form [tex]a^2-b^2[/tex], let us apply the identity [tex]a^2-b^2=(a+b)(a-b)[/tex]
Thus, we have;
[tex]\left(4 x^{4}+1\right)\left(4 x^{4}-1\right)[/tex] ------ (1)
Now, we shall factor the term [tex]4x^4-1[/tex]
[tex]4x^4-1=(2x^2)^2-1^2[/tex]
[tex]=(2x^2+1)(2x^2-1)[/tex]
Substituting the above expression in equation (1), we have;
[tex]\left(4 x^{4}+1\right)\left(2 x^{2}+1\right)(2x^2-1)[/tex]
Therefore, the factor of the given expression is [tex]\left(4 x^{4}+1\right)\left(2 x^{2}+1\right)(2x^2-1)[/tex]
Hence, Option B is the correct answer.
Given:
The given expression is
We need to determine the factor of the given expression.
Factor:
Let us rewrite the given expression.
Thus, we have;
Since, the above expression is of the form , let us apply the identity
Thus, we have;
------ (1)
Now, we shall factor the term
Substituting the above expression in equation (1), we have;
Therefore, the factor of the given expression is
Hence, Option B is the correct answer.
