Sure, let's factorize the expression [tex]\( 16a^2 - 25b^2 \)[/tex].
1. Identify the form: The given expression is [tex]\( 16a^2 - 25b^2 \)[/tex]. Notice that this is a difference of squares. The difference of squares formula is [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex].
2. Rewrite each term as a square:
- [tex]\( 16a^2 \)[/tex] can be rewritten as [tex]\( (4a)^2 \)[/tex] since [tex]\( (4a) \times (4a) = 16a^2 \)[/tex].
- [tex]\( 25b^2 \)[/tex] can be rewritten as [tex]\( (5b)^2 \)[/tex] since [tex]\( (5b) \times (5b) = 25b^2 \)[/tex].
3. Apply the difference of squares formula:
- The expression [tex]\( (4a)^2 - (5b)^2 \)[/tex] fits the difference of squares form where [tex]\( a = 4a \)[/tex] and [tex]\( b = 5b \)[/tex].
4. According to the difference of squares formula [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex], substitute [tex]\( 4a \)[/tex] for [tex]\( a \)[/tex] and [tex]\( 5b \)[/tex] for [tex]\( b \)[/tex]:
[tex]\[
(4a)^2 - (5b)^2 = (4a - 5b)(4a + 5b)
\][/tex]
Thus, the factorized form of the expression [tex]\( 16a^2 - 25b^2 \)[/tex] is:
[tex]\[
(4a - 5b)(4a + 5b)
\][/tex]
