Question

Which shows the difference p^2 + 6p + 2 / 4p^2 - 10p^2 / 4p^2?

a) -3p^2 + 2 / 4p^2
b) -9p^2 - 4p - 8 / 4p^2
c) 11p^2 + 6p + 2 / 4p^2
d) -9p^2 + 6p + 2 / 4p^2

Answer 1

The correct difference of the given algebraic expressions is found by combining like terms and simplifying over the common denominator, resulting in the answer 11p^2 + 6p + 2 over 4p^2.

Option c.

Step-by-step explanation:

The problem given is a simplification of algebraic expressions, which can be solved by combining like terms and simplifying.

We're asked to find the difference of p^2 + 6p + 2 and -10p^2, both over a denominator of 4p^2. To find this difference, you subtract the numerators while keeping the common denominator:

First, combine like terms in the numerator: (p^2 + 6p + 2) - (-10p^2) becomes p^2 + 10p^2 + 6p + 2, as subtracting a negative is the same as adding.

Then, simplify the combined terms: p^2 + 10p^2 is 11p^2, so the numerator is now 11p^2 + 6p + 2.

Finally, write the simplified expression over the original denominator: 11p^2 + 6p + 2 over 4p^2.

The correct answer is therefore option (c) 11p^2 + 6p + 2 / 4p^2.