Sure! Let's factor the given expression step-by-step.
The expression we need to factor is:
[tex]\[ 25x^2 - 16y^2 \][/tex]
Notice that this expression fits the form of a difference of squares, which is:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In our expression [tex]\( 25x^2 - 16y^2 \)[/tex], we can identify [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex] as follows:
[tex]\[ 25x^2 = (5x)^2 \][/tex]
[tex]\[ 16y^2 = (4y)^2 \][/tex]
So, we can rewrite the expression as:
[tex]\[ (5x)^2 - (4y)^2 \][/tex]
Now, applying the difference of squares formula:
[tex]\[ (5x)^2 - (4y)^2 = (5x - 4y)(5x + 4y) \][/tex]
Hence, the factored form of the expression [tex]\( 25x^2 - 16y^2 \)[/tex] is:
[tex]\[ (5x - 4y)(5x + 4y) \][/tex]
