# When do I apply the distributive property?

I'm a bit lost here....

Equation 1: $$(5p − 6) + (1 − p)$$.

Shouldn't I apply distributive property here? By distributing the '$$+$$' sign into $$(1 - p)$$ to give $$(1 + p)$$? If that is the case, then the new formula reworded is: $$(5p - 6) + 1 + p = 6p - 5,$$ right?

But the book has a different answer and it is, $$4p - 5$$ instead.... deductively examining where I went wrong, it seems the '$$+$$' sign isn't distributed and thus the $$p$$ in $$(1 - p)$$ didn't change into a positive

If the book has the right answer, then this procs my title question, when do we use distributive property?

Consider the following equation: $$−10 − 4(n − 5),$$ the $$-4$$ is distributed into $$n$$ and $$-5$$.... If I'm seeing how the formula is worded, whats the difference between this and the case above? Don't they both prompt distributive property cycle? The above case just has an invisible $$+1$$ right?

I got all the wrong answers in my math test on this part lol but i'm determined to know why.

• Why do you think that $(1-p)$ will become $(1+p)$ ? $(5p − 6) + (1 − p)= 5p-6+1-p$. – Mauro ALLEGRANZA Oct 19 '18 at 9:26
• i thought the + has an invisible 1 that it can distribute... is this not true? but then again whenever a positive times a negative it'll still be a negative anyways, so p won't turn positive i believe, just figured this out now lol – Moorease Oct 19 '18 at 9:32
• $1(1 - p) = 1 \cdot 1 + 1 \cdot (-p) = 1 - p$. – N. F. Taussig Oct 19 '18 at 9:45