Factorise 5x²-125
5(x^2-25)
5(x-5)(x+5)
2xpe power -8x
To factorize the expression 5x² - 125, first, we look for the greatest common factor (GCF) between the terms. In this case, both terms are divisible by 5. So, we can factor out 5 from both terms:
5(x² - 25)
Next, we notice that the expression inside the parentheses is a difference of squares. It can be written as:
5(x - 5)(x + 5)
So the fully factorized form of 5x² - 125 is 5(x - 5)(x + 5).
To factorize the expression 5x²-125, we can start by noticing that both terms are perfect squares.
The first term, 5x², can be written as (sqrt(5x))² or (sqrt(5))^2 * (x)^2.
The second term, 125, is a perfect cube of 5. It can be written as (sqrt(5))^3.
Therefore, we have:
5x²-125 = (sqrt(5)x)^2 - (sqrt(5))^3 = (sqrt(5)x)^2 - (sqrt(5))^2 * sqrt(5) = (sqrt(5)x)^2 - (sqrt(5))^2 * (sqrt(5)) = (sqrt(5)x)^2 - 5 * (sqrt(5))^2
Now, we can notice that both terms have a common factor of (sqrt(5)). We can factor it out:
5x²-125 = (sqrt(5))^2 * (x^2 - 5)
Finally, we can further factor the expression x² - 5 as the difference of squares:
5x²-125 = (sqrt(5))^2 * (x^2 - 5) = 5 * (x + sqrt(5)) * (x - sqrt(5))