1) $$ 4 a^{2}+9 b^{2}-12 a b $$

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The expression you provided is:

$$ 4 a^{2} + 9 b^{2} - 12 a b $$

We can factor this as a perfect square trinomial. Notice that it resembles the standard form:

$$ (pa + qb)^2 = p^2 a^2 + q^2 b^2 + 2 p q a b $$

Let's compare the given expression to the standard form:

1. **Identify $$ p $$ and $$ q $$:**
   - The coefficient of $$ a^2 $$ is $$ 4 $$, so $$ p^2 = 4 $$ which gives $$ p = 2 $$.
   - The coefficient of $$ b^2 $$ is $$ 9 $$, so $$ q^2 = 9 $$ which gives $$ q = 3 $$.

2. **Determine the cross term:**
   - The cross term in the expansion is $$ 2 p q a b $$.
   - Substituting $$ p = 2 $$ and $$ q = 3 $$, we get $$ 2 \times 2 \times 3 \times a b = 12 a b $$.

3. **Adjust for the sign:**
   - The given cross term is $$ -12 a b $$, which means our binomial will have a subtraction:
   $$ (2a - 3b)^2 $$

4. **Verify the factoring:**
   $$ (2a - 3b)^2 = 4a^2 - 12ab + 9b^2 $$

This matches the original expression.

**Final Factored Form:**

$$ 4 a^{2} + 9 b^{2} - 12 a b = (2a - 3b)^2 $$

**Answer:**

After factoring, the expression is equal to (2 a – 3 b) squared. Thus,

(2a − 3b)²
The expression $$ 4a^{2} + 9b^{2} - 12ab $$ can be factored as $$ (2a - 3b)^2 $$.

1) \( 4 a^{2}+9 b^{2}-12 a b \)

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