the answer is 16a2-4a+4a-1
it can be simplified to 16a2-1, which can be factored to
(4a+1)(4a-1)
Only the polynomial 16a² – 4a + 4a – 1 can be simplified to a difference of squares.
In math, the factoring or factorization is used to write an algebraic expression in factors. There are some rules for the factorization. One of them, it refers a difference of squares. The factoring rules shows that the difference of squares: a² – b² = (a – b)(a + b).
For solving this question, you should simplify the quadratic equation and identify if it is possible to write the equation as a difference of squares.
10a² + 3a – 3a – 16= (10a²-16)= 2(5a²-8)
It is not possible to write the equation as a difference of squares, since the both terms (5a²-8) are not perfect square.
It is possible to write the equation as a difference of squares, since the both terms (16a²-1)) are perfect square. Therefore, 16a²-1= (4a+1) (4a-1).
25a² + 6a – 6a + 36= 25a² + 36
It is not possible to write the equation as a difference of squares, because between the terms (25a² + 36) you have a sum.
24a² – 9a + 9a + 4= 24a² + 4
It is not possible to write the equation as a difference of squares, because between the terms (24a² + 4) you have a sum.
Read more about the difference of squares here:
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