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Simplify [tex]$\left(x^2+16\right)\left(x^2-16\right)$[/tex].

A. [tex]$x^4-32$[/tex]

B. [tex][tex]$x^4+32$[/tex][/tex]

C. [tex]$x^4+256$[/tex]

D. [tex]$x^4-256$[/tex]

Sagot :

GinnyAnswer
To simplify [tex]\((x^2 + 16)(x^2 - 16)\)[/tex], we can start by recognizing that this expression is a difference of squares. The difference of squares formula is given by:

[tex]\[ (a^2 - b^2) = (a - b)(a + b) \][/tex]

In this case, we let [tex]\(a = x^2\)[/tex] and [tex]\(b = 16\)[/tex]. Applying the difference of squares formula, we get:

[tex]\[ (x^2 + 16)(x^2 - 16) = (x^2)^2 - (16)^2 \][/tex]

Now, we simplify each term:

[tex]\[ (x^2)^2 = x^4 \][/tex]

[tex]\[ (16)^2 = 256 \][/tex]

Substituting these back into the expression, we obtain:

[tex]\[ (x^2 + 16)(x^2 - 16) = x^4 - 256 \][/tex]

Therefore, the simplified form of [tex]\((x^2 + 16)(x^2 - 16)\)[/tex] is [tex]\(x^4 - 256\)[/tex].

The best answer is:
D. [tex]\(x^4 - 256\)[/tex]
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