Question

1. which expression has more terms? explain how you know.

$a + 2b + 3c + 4d + 5$
$a + (b + b) + (c + c + c) + (d + d + d + d) + (1 + 1 + 1 + 1 + 1)$

Explanation:

Step1: Count terms in first expression

Identify individual terms separated by +: $a$, $2b$, $3c$, $4d$, $5$. Total terms: $5$.

Step2: Count terms in second expression

Identify individual terms separated by +: $a$, $b$, $b$, $c$, $c$, $c$, $d$, $d$, $d$, $d$, $1$, $1$, $1$, $1$, $1$. Total terms: $1+2+3+4+5=15$.

Step3: Compare the two totals

$15 > 5$

Answer:

The second expression $a+(b+b)+(c+c+c)+(d+d+d+d)+(1+1+1+1+1)$ has more terms. The first expression has 5 distinct terms, while the second expression has 15 individual terms when the grouped terms are counted separately.