Part A: Option e: [tex]5(9 x+1)[/tex]
Option f: [tex]45 x+5[/tex]
Part B: Option c: [tex]15(3 x+1)[/tex]
Option d: [tex](5 \cdot 9 x)+(5 \cdot 3)[/tex]
Part C: Option a: [tex](5 \cdot 9 x)-(5 \cdot 3)[/tex]
Option b: [tex]45 x-15[/tex]
Explanation:
Part A: The equation is [tex](5 \cdot 9 x)+(5 \cdot 1)[/tex]
Simplifying, we have,
[tex]45x+5[/tex]
Taking the term 5 common out, we have,
[tex]5(9 x+1)[/tex]
Thus, the above two expressions are equivalent to the equation [tex](5 \cdot 9 x)+(5 \cdot 1)[/tex].
Hence, Option e and Option f are the correct answers.
Part B: The equation is [tex]45 x+15[/tex]
Taking the term 15 common out, we have,
[tex]15(3 x+1)[/tex]
Also, the equation can be rewritten as,
[tex](5 \cdot 9 x)+(5 \cdot 3)[/tex]
Thus, the above two expressions are equivalent to the equation [tex]45 x+15[/tex]
Hence, Option c and Option d are the correct answers.
Part C: The equation is [tex]15(3 x-1)[/tex]
Multiplying, we have,
[tex]45 x-15[/tex]
The above expression can be rewritten as,
[tex](5 \cdot 9 x)-(5 \cdot 3)[/tex]
Thus, the above two expressions are equivalent to the equation [tex]15(3 x-1)[/tex]
Hence, Option a and Option b are the correct answers.
