Factorize `5-20x^2`

Answer

To factorize the expression \( 5 - 20x^2 \), we can follow these steps:

### Step 1: Identify the common factor
First, we observe that both terms in the expression \( 5 \) and \( -20x^2 \) have a common factor. The common factor here is \( 5 \).

### Step 2: Factor out the common factor
We factor \( 5 \) out of the expression:
\[ 5 - 20x^2 = 5(1 - 4x^2) \]

### Step 3: Recognize the difference of squares
Next, we notice that \( 1 - 4x^2 \) can be expressed as a difference of squares. We can rewrite \( 4x^2 \) as \( (2x)^2 \):
\[ 1 - 4x^2 = 1 - (2x)^2 \]

### Step 4: Apply the difference of squares formula
The difference of squares can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a = 1 \) and \( b = 2x \):
\[ 1 - (2x)^2 = (1 - 2x)(1 + 2x) \]

### Step 5: Combine the factors
Now, we can combine this with the common factor we factored out in Step 2:
\[ 5(1 - 4x^2) = 5(1 - 2x)(1 + 2x) \]

### Final Answer
Thus, the fully factored form of \( 5 - 20x^2 \) is:
\[ 5(1 - 2x)(1 + 2x) \]

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