Question

(a) select all equivalent expressions from the list for the expression.
5x + 25
□ 5·x + 5·5 □ 5(x + 5) □ 5(5x + 1) □ 30x

(b) select all equivalent expressions from the list for the expression.
13 + 10y − 8 − y
□ 9 + 5y □ 5y + 9y □ 5y + 9 □ 9y + 5

Explanation:

Step1: Analyze part (a) options

First expression: $5 \cdot x + 5 \cdot 5 = 5x + 25$, matches the original.
Second expression: Use distributive property: $5(x+5)=5x+5\cdot5=5x+25$, matches the original.
Third expression: $5(5x+1)=25x+5$, does not match.
Fourth expression: $30x$ is not equal to $5x+25$, does not match.

Step2: Simplify part (b) original expression

Combine constant terms: $13-8=5$.
Combine like variable terms: $10y-y=9y$.
Simplified form: $9y+5$.
Now check options:
$9+5y$ does not match; $5y+9y=14y$ does not match; $5y+9$ does not match; $9y+5$ matches.

Answer:

(a) $5 \cdot x + 5 \cdot 5$, $5(x+5)$
(b) $9y + 5$