Perfect Squares
Perfect square formula/rules:
- [tex]a^2+2ab+b^2=(a+b)^2[/tex]
- [tex]a^2-2ab+b^2=(a-b)^2[/tex]
Trinomials are often organized like [tex]ax^2+bx+c[/tex].
The b value in this case is c, and it will always equal the square of half of the b value.
- Perfect square trinomial: [tex]ax^2+bx+(\dfrac{b}{2})^2[/tex]
- or [tex]ax^2-bx+(\dfrac{b}{2})^2[/tex]
Solving the Question
We're given:
In a trinomial, we're given the [tex]ax^2[/tex] and [tex]bx[/tex] values. a in this case is 1 and b in this case is 4. To find the third value by dividing 4 by 2 and squaring the quotient:
Therefore, the term that we can add is + 4.
[tex]c^2-4c+4[/tex]
To write this as the square of a bracketed expression, we can follow the rule [tex]a^2-2ab+b^2=(a-b)^2[/tex]:
[tex](c-2)^2[/tex]
Answer
[tex]c^2-4c+4[/tex]
[tex](c-2)^2[/tex]
