Answered

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5. Which expresses the correct factorization of [tex]$25x^2 - 49$[/tex]?

A. [tex](5x+7)^2[/tex]
B. [tex](5x-7)^2[/tex]
C. [tex](5x+7)^2(5x-7)[/tex]
D. [tex](5x-7)(5x+7)[/tex]

Sagot :

GinnyAnswer
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]
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