a^2+4a+4 2. 6x^2+22x+12 3. 8a^2-2a-1 u b^2+4b-5 square 16-49a^2

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Answer 1

Let's factor each expression step by step:1.

This is a perfect square trinomial. It can be factored as:

2.

First, factor out the greatest common factor (GCF), which is 2:

Next, factor the quadratic inside the parentheses:

We need to find two numbers that multiply to

and add up to 11. These numbers are 9 and 2.So, we can rewrite the quadratic as:

Now, factor by grouping:

Thus, the factored form is:

3.

This quadratic does not factor nicely with integer coefficients. We can use the quadratic formula to find the roots if needed:

where

,

, and

.4.

We need to find two numbers that multiply to

and add up to

. These numbers are

and

.So, we can rewrite the quadratic as:

Now, factor by grouping:

Thus, the factored form is:

5.

This is a difference of squares. It can be factored as:

So, the factored form is:

In summary:1. \( (a + 2)^2 \)2. \( 2(3x + 2)(x + 3) \)3.

(no simple factorization)4. \( (b - 1)(b + 5) \)5. \( (4 - 7a)(4 + 7a) \)

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