Question

25x^6 - 9x^4 + 100x^2 - 36

Answer 1

(25x^4 + 4)(x - 3)(x + 3)

Explanation:

First, notice that there are common factors within pairs of terms:

Group the first two terms and the last two terms:

(25x^6 - 9x^4) + (100x^2 - 36)

Factor out the greatest common factor from each group:

25x^4(x^2 - 9) + 4(25x^2 - 9)

Now, notice that you have a common factor of (x^2 - 9) in both terms:

(25x^4 + 4)(x^2 - 9)

Further factor the difference of squares x^2 - 9:

(25x^4 + 4)(x - 3)(x + 3)

So, the factored form of the expression 25x^6 - 9x^4 + 100x^2 - 36 is (25x^4 + 4)(x - 3)(x + 3).