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# Factor trinomial $$ \color{blue}{ 4x^2-12x+9 } $$

## Answer

The factored form is $$ \color{blue}{ 4x^2-12x+9 = \left(2x-3\right)^2 } $$

## Explanation

Both the first and third terms are perfect squares.

$$ 4x^2 = \left( \color{blue}{ 2x } \right)^2 ~~ \text{and} ~~ 9 = \left( \color{red}{ 3 } \right)^2 $$

The middle term ( $ -12x $ ) is two times the product of the terms that are squared.

$$ -12x = - 2 \cdot \color{blue}{2x} \cdot \color{red}{3} $$

We can conclude that the polynomial $ 4x^{2}-12x+9 $ is a **perfect square trinomial**, so we will use the formula below.

$$ A^2 - 2AB + B^2 = (A - B)^2 $$

In this example we have $ \color{blue}{ A = 2x } $ and $ \color{red}{ B = 3 } $ so,

$$ 4x^{2}-12x+9 = ( \color{blue}{ 2x } - \color{red}{ 3 } )^2 $$