Question

Factor the perfect square trinomials. Write your answer in the form of (a+b)2
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 into the required forms, we can use the general formulas:

1. \( a^2 + 2ab + b^2 = (a + b)^2 \)
2. \( a^2 - 2ab + b^2 = (a - b)^2 \)

Let's factor each of the given trinomials:

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

Here, \( a = x \) and \( b = 3 \) (since \( b^2 = 9 \)).

So, \( x^2 + 6x + 9 = (x + 3)^2 \)

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

Here, \( a = x \) and \( b = 5 \) (since \( b^2 = 25 \)).

So, \( x^2 + 10x + 25 = (x + 5)^2 \)

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

Here, \( a = 3x \) and \( b = 2 \) (since \( b^2 = 4 \)).

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

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

Here, \( a = 3x \) and \( b = 5 \) (since \( b^2 = 25 \)).

So, \( 9x^2 - 30x + 25 = (3x - 5)^2 \)

Now, summarizing the factorizations:

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