To factor the expression [tex]\( 25x^2 - 49 \)[/tex], let's follow the steps for factoring a difference of squares.
1. Identify the terms: The given expression is [tex]\( 25x^2 - 49 \)[/tex]. Notice that both terms are perfect squares:
[tex]\[ 25x^2 = (5x)^2 \][/tex]
[tex]\[ 49 = 7^2 \][/tex]
2. Apply the difference of squares formula: The difference of squares formula is given by:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
Here, [tex]\( a = 5x \)[/tex] and [tex]\( b = 7 \)[/tex].
3. Write the expression in the difference of squares form:
[tex]\[ 25x^2 - 49 = (5x)^2 - 7^2 \][/tex]
4. Apply the formula:
[tex]\[ (5x)^2 - 7^2 = (5x - 7)(5x + 7) \][/tex]
So, the correct factorization of [tex]\( 25x^2 - 49 \)[/tex] is:
[tex]\[
(5x - 7)(5x + 7)
\][/tex]
Answer:
[tex]\[
(5 x - 7)(5 x + 7)
\][/tex]
