Answer :
To solve the expression [tex]\(52x - 169\)[/tex] and find its equivalent form, we want to factor it in a way that matches the given template: [tex]\(13 \square\)[/tex].
Here's how you do it step-by-step:
1. Identify Common Factor: Notice that both terms in the expression, [tex]\(52x\)[/tex] and [tex]\(-169\)[/tex], are divisible by 13. This suggests that 13 is a common factor.
2. Factor Out 13:
- Divide each term by 13:
- For the term [tex]\(52x\)[/tex], divide 52 by 13, which gives us [tex]\(4x\)[/tex].
- For the term [tex]\(-169\)[/tex], divide [tex]\(-169\)[/tex] by 13, which gives us [tex]\(-13\)[/tex].
3. Express the Original Expression:
- Combine the results from the division by 13:
- [tex]\[52x - 169 = 13(4x - 13)\][/tex]
4. Conclusion:
- Thus, the expression [tex]\(52x - 169\)[/tex] is equivalent to [tex]\(13(4x - 13)\)[/tex].
So, the missing part in the box, [tex]\(\square\)[/tex], is [tex]\((4x - 13)\)[/tex].
Here's how you do it step-by-step:
1. Identify Common Factor: Notice that both terms in the expression, [tex]\(52x\)[/tex] and [tex]\(-169\)[/tex], are divisible by 13. This suggests that 13 is a common factor.
2. Factor Out 13:
- Divide each term by 13:
- For the term [tex]\(52x\)[/tex], divide 52 by 13, which gives us [tex]\(4x\)[/tex].
- For the term [tex]\(-169\)[/tex], divide [tex]\(-169\)[/tex] by 13, which gives us [tex]\(-13\)[/tex].
3. Express the Original Expression:
- Combine the results from the division by 13:
- [tex]\[52x - 169 = 13(4x - 13)\][/tex]
4. Conclusion:
- Thus, the expression [tex]\(52x - 169\)[/tex] is equivalent to [tex]\(13(4x - 13)\)[/tex].
So, the missing part in the box, [tex]\(\square\)[/tex], is [tex]\((4x - 13)\)[/tex].
