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=

Skip to navigation

page 3 of 3

Answer 1

To factor the perfect square trinomials, we can use the formulas:

\[ (a + b)^2 = a^2 + 2ab + b^2 \] \[ (a - b)^2 = a^2 - 2ab + b^2 \]

Now we will factor each trinomial:

1. \(x^2 + 6x + 9\)
   We recognize this as the expansion of \((x + 3)^2\).

   \[ x^2 + 6x + 9 = (x + 3)^2 \]

2. \(x^2 + 10x + 25\)
   This is the expansion of \((x + 5)^2\).

   \[ x^2 + 10x + 25 = (x + 5)^2 \]

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

   \[ 9x^2 + 12x + 4 = (3x + 2)^2 \]

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

   \[ 9x^2 - 30x + 25 = (3x - 5)^2 \]

Putting it all together, the factored forms of the given perfect square trinomials are:

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