Final answer:
The factored form of the quadratic equation 16p^2 - 100 is found using the difference of squares, resulting in the correct expression of (4p + 10)(4p - 10), which corresponds to option a.
Step-by-step explanation:
The question asks which expression is a factor of the quadratic equation 16p^2 - 100. To find this, we should recognize that the equation is a difference of squares, which can be factored into the product of a sum and difference of the square roots of each term.
The square root of 16p^2 is 4p and the square root of 100 is 10. Therefore, the factored form of the equation is (4p + 10)(4p - 10). Out of the given options, option a presents this correct factored expression.
To solve the mathematical problem completely, we can apply the difference of squares factoring rule:
16p^2 - 100 = (4p)^2 - 10^2
= (4p + 10)(4p - 10)
Therefore, the correct option in the final answer is option a.