Answer :
Certainly! To solve the expression [tex]\(169m^2 - 4u^2\)[/tex], we can use the difference of squares formula. The difference of squares formula is:
[tex]\[ a^2 - b^2 = (a + b)(a - b) \][/tex]
Here's how we apply this to the given expression:
1. Identify the squares:
- The term [tex]\(169m^2\)[/tex] is a perfect square because it can be written as [tex]\((13m)^2\)[/tex].
- The term [tex]\(4u^2\)[/tex] is also a perfect square because it can be written as [tex]\((2u)^2\)[/tex].
2. Apply the difference of squares formula:
- Let [tex]\(a = 13m\)[/tex] and [tex]\(b = 2u\)[/tex].
- Substitute into the difference of squares formula:
[tex]\[
(13m + 2u)(13m - 2u)
\][/tex]
3. Conclusion:
The expression [tex]\(169m^2 - 4u^2\)[/tex] can be factored into [tex]\((13m + 2u)(13m - 2u)\)[/tex].
That's how we factor the expression using the difference of squares!
[tex]\[ a^2 - b^2 = (a + b)(a - b) \][/tex]
Here's how we apply this to the given expression:
1. Identify the squares:
- The term [tex]\(169m^2\)[/tex] is a perfect square because it can be written as [tex]\((13m)^2\)[/tex].
- The term [tex]\(4u^2\)[/tex] is also a perfect square because it can be written as [tex]\((2u)^2\)[/tex].
2. Apply the difference of squares formula:
- Let [tex]\(a = 13m\)[/tex] and [tex]\(b = 2u\)[/tex].
- Substitute into the difference of squares formula:
[tex]\[
(13m + 2u)(13m - 2u)
\][/tex]
3. Conclusion:
The expression [tex]\(169m^2 - 4u^2\)[/tex] can be factored into [tex]\((13m + 2u)(13m - 2u)\)[/tex].
That's how we factor the expression using the difference of squares!
