Question 242949
{{{4p^2 - q^2 + 2p + q}}} Start with the given expression.



{{{(4p^2 - q^2) + (2p + q)}}} Group the terms into pairs



{{{((2p)^2 - q^2) + (2p + q)}}} Rewrite {{{4p^2}}} as {{{(2p)^2}}}



{{{(2p+q)(2p-q) + (2p + q)}}} Factor the first group using the difference of squares formula.



{{{(2p+q)((2p-q) + 1)}}} Factor out the GCF {{{2p+q}}}



{{{(2p+q)(2p-q + 1)}}} Remove the inner parenthesis.



So {{{4p^2 - q^2 + 2p + q}}} completely factors to {{{(2p+q)(2p-q + 1)}}}



In other words, {{{4p^2 - q^2 + 2p + q=(2p+q)(2p-q + 1)}}}