(p+q)+(p+q)\( = \) A) \( 3(p+q) \) B) \( (p+q)^{3} \) C) \( p+q+p^{2}+q^{2} \) D) \( (p+q)(p+q+1 \) E) \( 2(p+q)^{2} \)

To solve the expression \((p+q) + (p+q)\), you can combine like terms. This turns into simply \(2(p+q)\). None of the options provided exactly state this result, but if you rearrange, the equivalent answer closest to our result that you would get from squaring or expanding would be \( \text{E: } 2(p+q)^{2} \) given \( 2(p+q) \). But remember, \( (p+q)(p+q) = (p+q)^{2} \). Another way to think about this is by using algebraic properties! For example, if \( p = 1 \) and \( q = 2 \), then \((p+q) + (p+q) = 3 + 3 = 6\). Applying the distributive property can help you avoid common mistakes here. Just take it step-by-step, and you'll find solutions more easily!