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

Question

(

+

)
2

or (a−b)2
(

−

)
2


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

2
+
6

+
9
=

2) x2+10x+25=

2
+
10

+
25
=

3) 9x2+12x+4=
9

2
+
12

+
4
=

4) 9x2−30x+25=
9

2
−
30

+
25
=

Answer 1

To factor the perfect square trinomials, we will determine if they can be expressed in the form \((a+b)^2\) or \((a-b)^2\).

1. \(x^2 + 6x + 9\)

To factor this: \[ x^2 + 6x + 9 = (x + 3)^2 \]

2. \(x^2 + 10x + 25\)

To factor this: \[ x^2 + 10x + 25 = (x + 5)^2 \]

3. \(9x^2 + 12x + 4\)

To factor this: \[ 9x^2 + 12x + 4 = (3x + 2)^2 \]

4. \(9x^2 - 30x + 25\)

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

So, summarizing the factors:

1. \(x^2 + 6x + 9 = (x + 3)^2\)

2. \(x^2 + 10x + 25 = (x + 5)^2\)

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

4. \(9x^2 - 30x + 25 = (3x - 5)^2\)