45a2 - 20 factorise using the difference of two squares

To factorize the expression \( 45a^2 - 20 \) using the difference of two squares, we start by factoring out the greatest common factor (GCF) from both terms.

### Step 1: Find the GCF
The GCF of \( 45a^2 \) and \( 20 \) is 5. So, we factor out 5 from the entire expression:
\[
45a^2 - 20 = 5(9a^2 - 4)
\]

### Step 2: Apply the difference of squares
Now we apply the difference of squares formula, which is:
\[
x^2 - y^2 = (x - y)(x + y)
\]
Here, \( 9a^2 - 4 \) is a difference of squares because:
\[
9a^2 = (3a)^2 \quad \text{and} \quad 4 = 2^2
\]

Thus, we can rewrite the expression as:
\[
9a^2 - 4 = (3a - 2)(3a + 2)
\]

### Step 3: Substitute back
Finally, we substitute this into our factored form:
\[
5(9a^2 - 4) = 5(3a - 2)(3a + 2)
\]

So, the fully factorized form is:
\[
45a^2 - 20 = 5(3a - 2)(3a + 2)
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factorize expressions that are not perfect squares?
2. What is the significance of the difference of two squares in factoring?
3. Can the difference of squares method be applied to cubic terms?
4. How do you factor quadratic expressions that are not a difference of squares?
5. How would you expand \( 5(3a - 2)(3a + 2) \) to verify the factorization?

**Tip:** Always look for a greatest common factor (GCF) before applying the difference of squares formula.

45a^2 - 20 factorise using the difference of two squares

Learn how to factorize the expression 45a^2 - 20 by first factoring out the greatest common factor (GCF) and then applying the difference of squares formula. This detailed solution is ideal for students in Grades 9-10 who are learning advanced algebra techniques.

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