Answer :
To factor the expression [tex]\( 25x^2 - 169y^2 \)[/tex] using the difference of squares formula, follow these steps:
1. Recognize the formula:
The difference of squares formula is given by:
[tex]\[
a^2 - b^2 = (a + b)(a - b)
\][/tex]
Here, you need to identify [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex] in the expression [tex]\( 25x^2 - 169y^2 \)[/tex].
2. Identify [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex]:
- [tex]\( a^2 = 25x^2 \)[/tex]
- [tex]\( b^2 = 169y^2 \)[/tex]
3. Find the square roots of [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex]:
- The square root of [tex]\( 25x^2 \)[/tex] is [tex]\( 5x \)[/tex] because [tex]\((5x)^2 = 25x^2\)[/tex].
- The square root of [tex]\( 169y^2 \)[/tex] is [tex]\( 13y \)[/tex] because [tex]\((13y)^2 = 169y^2\)[/tex].
4. Substitute into the difference of squares formula:
Using the values obtained for [tex]\( a \)[/tex] and [tex]\( b \)[/tex], substitute them back into the formula:
[tex]\[
25x^2 - 169y^2 = (5x)^2 - (13y)^2 = (5x + 13y)(5x - 13y)
\][/tex]
So, the factored form of [tex]\( 25x^2 - 169y^2 \)[/tex] is:
[tex]\[
(5x + 13y)(5x - 13y)
\][/tex]
1. Recognize the formula:
The difference of squares formula is given by:
[tex]\[
a^2 - b^2 = (a + b)(a - b)
\][/tex]
Here, you need to identify [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex] in the expression [tex]\( 25x^2 - 169y^2 \)[/tex].
2. Identify [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex]:
- [tex]\( a^2 = 25x^2 \)[/tex]
- [tex]\( b^2 = 169y^2 \)[/tex]
3. Find the square roots of [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex]:
- The square root of [tex]\( 25x^2 \)[/tex] is [tex]\( 5x \)[/tex] because [tex]\((5x)^2 = 25x^2\)[/tex].
- The square root of [tex]\( 169y^2 \)[/tex] is [tex]\( 13y \)[/tex] because [tex]\((13y)^2 = 169y^2\)[/tex].
4. Substitute into the difference of squares formula:
Using the values obtained for [tex]\( a \)[/tex] and [tex]\( b \)[/tex], substitute them back into the formula:
[tex]\[
25x^2 - 169y^2 = (5x)^2 - (13y)^2 = (5x + 13y)(5x - 13y)
\][/tex]
So, the factored form of [tex]\( 25x^2 - 169y^2 \)[/tex] is:
[tex]\[
(5x + 13y)(5x - 13y)
\][/tex]
