To factorize the expression [tex]\( 16x^2 - 25y^2 \)[/tex], we can recognize that it is a difference of squares. The difference of squares formula is:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In this given expression, we have:
[tex]\[ 16x^2 - 25y^2 \][/tex]
First, we observe that both [tex]\( 16x^2 \)[/tex] and [tex]\( 25y^2 \)[/tex] are perfect squares.
1. We identify the square roots of each term:
- The square root of [tex]\( 16x^2 \)[/tex] is [tex]\( 4x \)[/tex].
- The square root of [tex]\( 25y^2 \)[/tex] is [tex]\( 5y \)[/tex].
2. We now apply the difference of squares formula:
- We replace [tex]\( a \)[/tex] with [tex]\( 4x \)[/tex].
- We replace [tex]\( b \)[/tex] with [tex]\( 5y \)[/tex].
Using the formula [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex], we get:
[tex]\[ 16x^2 - 25y^2 = (4x - 5y)(4x + 5y) \][/tex]
Thus, the factorization of the expression [tex]\( 16x^2 - 25y^2 \)[/tex] is:
[tex]\[ (4x - 5y)(4x + 5y) \][/tex]
