Factor completely p^2 – 1 – 4q^2 – 4q

Question

This is a question from the unit on factoring polynomials in algebra 1 or algebra 2

Answer 1

p^2 – 1 – 4q^2 – 4q

= p^2 - (4q^2 + 4q + 1)

= p^2 - (2q+1)^2

From here, you may recognize that it is in a form of a^2 - b^2.

Can you continue to finish it on your own? Or let me know if you need further assistance. Good study!

Answer 2

Rearrange inside the brackets:

p² - (4q² + 4q + 1) now factor inside the brackets

p² - (2q +1) (2q +1)

p² - (2q + 1)²

This is the same as the difference of two squares a²- b² = (a-b)(a+b)

[p - (2q + 1)][p + (2q +1)] remove small brackets

[p - 2q - 1][p + 2q + 1]

Answer 3