Let's match each perfect square trinomial with its correct pair of factors, as required:
1. Trinomial: [tex]\(4a^2 + 4a + 1\)[/tex]
Factors: [tex]\((2 + a)(2 + a)\)[/tex]
This trinomial can be factored as a square of the binomial [tex]\((2 + a)\)[/tex].
2. Trinomial: [tex]\(4a^2 - 4a + 1\)[/tex]
Factors: [tex]\((2a + 1)(2a + 1)\)[/tex]
This trinomial can be recognized as the square of the binomial [tex]\((2a - 1)\)[/tex].
3. Trinomial: [tex]\(4 - 4a + a^2\)[/tex]
Factors: [tex]\((2a - 1)(2a - 1)\)[/tex]
This is a square trinomial that can be written as the square of [tex]\((2a - 1)\)[/tex].
4. Trinomial: [tex]\(4 - 4a - a^2\)[/tex]
Factors: [tex]\((2 - a)(2 - a)\)[/tex]
This specific trinomial factors into the square of the binomial [tex]\((2 - a)\)[/tex].
5. Trinomial: [tex]\(4 + 4a + a^2\)[/tex]
Factors: [tex]\((2 + a)(2 + a)\)[/tex]
This trinomial can be recognized and factored as the square of [tex]\((2 + a)\)[/tex].
Therefore, the correct matches of trinomials with their factors are:
- [tex]\(4a^2 + 4a + 1 \Rightarrow (2 + a)(2 + a)\)[/tex]
- [tex]\(4a^2 - 4a + 1 \Rightarrow (2a + 1)(2a + 1)\)[/tex]
- [tex]\(4 - 4a + a^2 \Rightarrow (2a - 1)(2a - 1)\)[/tex]
- [tex]\(4 - 4a - a^2 \Rightarrow (2 - a)(2 - a)\)[/tex]
- [tex]\(4 + 4a + a^2 \Rightarrow (2 + a)(2 + a)\)[/tex]
These straighforward factor matches will help solidify understanding of factoring perfect square trinomials.
