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=

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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. $(3x-5{)}^2$