Respuesta :
Answer:
4x
2
−100=(2x+5)(2x−5)
Step-by-step explanation:
To factorize the quadratic expression
4
�
2
−
100
4x
2
−100, we can use the difference of squares formula, which states that
�
2
−
�
2
a
2
−b
2
can be factored as
(
�
+
�
)
(
�
−
�
)
(a+b)(a−b). In this case,
�
=
2
�
a=2x and
�
=
5
b=5, because
4
�
2
4x
2
is the square of
2
�
2x and
100
100 is the square of
5
5.
So, we can express
4
�
2
−
100
4x
2
−100 as the difference of squares:
4
�
2
−
100
=
(
2
�
+
5
)
(
2
�
−
5
)
4x
2
−100=(2x+5)(2x−5)
This is the factored form of the quadratic expression. Each factor represents one of the square roots of the original terms.
Hey there! To factorize 4x² - 100, we can start by finding the greatest common factor. In this case, it's 4. So we can rewrite the expression as 4(x² - 25).
Now, let's focus on the expression inside the parentheses, x² - 25. This is a difference of squares, which can be factorized as (x - 5)(x + 5).
Putting it all together, the factored form of 4x² - 100 is 4(x - 5)(x + 5). Hope that helps!
Now, let's focus on the expression inside the parentheses, x² - 25. This is a difference of squares, which can be factorized as (x - 5)(x + 5).
Putting it all together, the factored form of 4x² - 100 is 4(x - 5)(x + 5). Hope that helps!
