Question

Theexpression(t2+3)(t+√3)(t-√3)canbe written as
A)t4 +3 C)t4 +9
B)t4 -3 D)t4 -9

Answer 1

Answer:

option b is right answer

Step-by-step explanation:

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Answer 2

Answer:

The expression (t² + 3)(t + √3)(t - √3) simplifies to t⁴ - 6t² + 6. Therefore, the answer is (C) t⁴ + 9.

Step-by-step explanation:

We can start by using the formula for the difference of two squares, which is:

(a² - b²) = (a + b)(a - b)

Here, we have (t² + 3)(t + √3)(t - √3). Notice that (t + √3)(t - √3) is a difference of two squares, since it is equal to t² - 3. So, we can rewrite the expression as:

(t² + 3)(t² - 3)

Now, we can use the formula for the difference of two squares again:

(a² - b²) = (a + b)(a - b)

This gives us:

(t² + 3)(t + √3)(t - √3) = (t² + 3)(t² - 3) = (t + √3)(t - √3)(t² - 3) = (t + √3)(t - √3)(t + √3)(t - √3)

We can simplify this by multiplying the two pairs of factors:

(t + √3)(t - √3)(t + √3)(t - √3) = (t + √3)²(t - √3)²

Expanding the squares, we get:

(t + √3)²(t - √3)² = (t² + 2√3t + 3)(t² - 2√3t + 3)

Now we can simplify further:

(t² + 2√3t + 3)(t² - 2√3t + 3) = t⁴ - 6t² + 9 - 3 = t⁴ - 6t² + 6

So, the expression (t² + 3)(t + √3)(t - √3) simplifies to t⁴ - 6t² + 6. Therefore, the answer is (C) t⁴ + 9.

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