Factor the perfect square trinomials

Question

(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, we use the formula:

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

Now, let's factor the given trinomials:

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

Here, \( a = x \) and \( b = 3 \) (because \( 3^2 = 9 \) and \( 2ab = 6x \) implies \( 2 \cdot x \cdot 3 = 6x \)). Thus, we have: \[ x^2 + 6x + 9 = (x + 3)^2 \]

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

Here, \( a = x \) and \( b = 5 \) (because \( 5^2 = 25 \) and \( 2ab = 10x \)). Thus, we have: \[ x^2 + 10x + 25 = (x + 5)^2 \]

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

Here, \( a = 3x \) and \( b = 2 \) (because \( 2^2 = 4 \) and \( 2ab = 12x \) implies \( 2 \cdot 3x \cdot 2 = 12x \)). Thus, we have: \[ 9x^2 + 12x + 4 = (3x + 2)^2 \]

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

Here, \( a = 3x \) and \( b = 5 \) (because \( 5^2 = 25 \) and \( 2ab = -30x \)). Thus, we have: \[ 9x^2 - 30x + 25 = (3x - 5)^2 \]

So the factorizations are:

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

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

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

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

Answer 2

does the answer have to be double quotationed?

Answer 3

No, the answers do not need to be double-quoted. You can present the factorizations without quotes. Here are the factorizations again without quotes:

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

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

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

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

Feel free to format them as you prefer!