Certainly! Let's carefully translate each phrase into its corresponding algebraic expression.
1. Phrase: "Eight more than a number cubed"
- Explanation: This phrase indicates that we take a number [tex]\( n \)[/tex], cube it ([tex]\( n^3 \)[/tex]), and then add eight to the result.
- Algebraic Expression: [tex]\( n^3 + 8 \)[/tex]
- Matching expression: [tex]\( 8 + n^3 \)[/tex]
2. Phrase: "The difference of eight and twice a number"
- Explanation: This phrase indicates we start with eight and subtract twice the number ([tex]\( 2n \)[/tex]) from it.
- Algebraic Expression: [tex]\( 8 - 2n \)[/tex]
- Matching expression: [tex]\( 8 - 2n \)[/tex]
3. Phrase: "The quotient of eight and a number increased by two"
- Explanation: This phrase indicates dividing eight by the result of a number [tex]\( n \)[/tex] increased by two.
- Algebraic Expression: [tex]\( \frac{8}{n + 2} \)[/tex]
- Matching expression: [tex]\( \frac{8}{n + 2} \)[/tex]
4. Phrase: "Eight less than a number squared"
- Explanation: This phrase indicates squaring a number [tex]\( n \)[/tex] and then subtracting eight from the result.
- Algebraic Expression: [tex]\( n^2 - 8 \)[/tex]
- Matching expression: [tex]\( n^2 - 8 \)[/tex]
Therefore, the matches are:
1. "Eight more than a number cubed" [tex]$\rightarrow$[/tex] [tex]\( 8 + n^3 \)[/tex]
2. "The difference of eight and twice a number" [tex]$\rightarrow$[/tex] [tex]\( 8 - 2n \)[/tex]
3. "The quotient of eight and a number increased by two" [tex]$\rightarrow$[/tex] [tex]\( \frac{8}{n + 2} \)[/tex]
4. "Eight less than a number squared" [tex]$\rightarrow$[/tex] [tex]\( n^2 - 8 \)[/tex]
Hence, the final result is:
- "Eight more than a number cubed" matches with [tex]\( 8 + n^3 \)[/tex]
- "The difference of eight and twice a number" matches with [tex]\( 8 - 2n \)[/tex]
- "The quotient of eight and a number increased by two" matches with [tex]\( \frac{8}{n + 2} \)[/tex]
- "Eight less than a number squared" matches with [tex]\( n^2 - 8 \)[/tex]
