Factor the perfect square trinomials. Write your answer in the form of (a+b)2

Question

or (a−b)2


(1 point)
1) x2+6x+9=

2) x2+10x+25=

3) 9x2+12x+4=

4) 9x2−30x+25=

Answer 1

To factor the perfect square trinomials in the requested form, we will identify the binomial that, when squared, gives us the trinomial.

1. \( x^2 + 6x + 9 \) can be factored as: \[ (x + 3)^2 \]

2. \( x^2 + 10x + 25 \) can be factored as: \[ (x + 5)^2 \]

3. \( 9x^2 + 12x + 4 \) can be factored as: \[ (3x + 2)^2 \]

4. \( 9x^2 - 30x + 25 \) can be factored as: \[ (3x - 5)^2 \]

So the final answers are:

1. \( (x + 3)^2 \)

2. \( (x + 5)^2 \)

3. \( (3x + 2)^2 \)

4. \( (3x - 5)^2 \)