Question

If g(x)=(x2+1)(x2−1)g(x)=(x2+1)(x2−1) Question 5 options: a) 4x3−14x3-1 b) 4x34x3 c) 4x24x2 d) 4x3+4x4x3+4x e) 4x3+4x−14x3+4x-1

Answer 1

To simplify the expression g(x) = (x^2+1)(x^2-1), you can use the difference of squares identity. The correct answer is option d) 4x^3+4x.

Step-by-step explanation:

To simplify the expression g(x) = (x^2+1)(x^2-1), we can use the difference of squares identity, which states that a^2 - b^2 = (a+b)(a-b). Applying this identity, we get:

g(x) = (x^2+1)(x^2-1) = (x+1)(x-1)(x^2-1)

Further simplifying, we have:

g(x) = (x+1)(x-1)(x^2-1) = (x+1)(x-1)(x+1)(x-1)

Using the distributive property, we expand:

g(x) = (x+1)(x-1)(x+1)(x-1) = (x+1)(x+1)(x-1)(x-1)

Finally, we can rewrite g(x) as:

g(x) = (x+1)^2(x-1)^2 = (x+1)(x+1)(x-1)(x-1)

So the correct answer is option d) 4x^3+4x.

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