Answer :
We begin with the quadratic expression
[tex]$$
36s^2 - 60s + 25.
$$[/tex]
Notice that this expression can be thought of as a perfect square trinomial. A perfect square trinomial has the form
[tex]$$
(as - b)^2 = a^2s^2 - 2ab\,s + b^2.
$$[/tex]
First, compare the coefficient of [tex]$s^2$[/tex] in the given expression with [tex]$a^2$[/tex]. Since [tex]$a^2 = 36$[/tex], we have
[tex]$$
a = 6.
$$[/tex]
Next, we compare the constant term with [tex]$b^2$[/tex]. The constant is [tex]$25$[/tex], so
[tex]$$
b^2 = 25 \quad \Longrightarrow \quad b = 5.
$$[/tex]
Now, check the middle term. For the binomial squared, the middle term is given by [tex]$-2ab\,s$[/tex]. Substituting the found values,
[tex]$$
-2ab\,s = -2(6)(5)s = -60s,
$$[/tex]
which matches the middle term of the given expression.
Since all three terms match, we can factor the quadratic completely as
[tex]$$
(6s - 5)^2.
$$[/tex]
[tex]$$
36s^2 - 60s + 25.
$$[/tex]
Notice that this expression can be thought of as a perfect square trinomial. A perfect square trinomial has the form
[tex]$$
(as - b)^2 = a^2s^2 - 2ab\,s + b^2.
$$[/tex]
First, compare the coefficient of [tex]$s^2$[/tex] in the given expression with [tex]$a^2$[/tex]. Since [tex]$a^2 = 36$[/tex], we have
[tex]$$
a = 6.
$$[/tex]
Next, we compare the constant term with [tex]$b^2$[/tex]. The constant is [tex]$25$[/tex], so
[tex]$$
b^2 = 25 \quad \Longrightarrow \quad b = 5.
$$[/tex]
Now, check the middle term. For the binomial squared, the middle term is given by [tex]$-2ab\,s$[/tex]. Substituting the found values,
[tex]$$
-2ab\,s = -2(6)(5)s = -60s,
$$[/tex]
which matches the middle term of the given expression.
Since all three terms match, we can factor the quadratic completely as
[tex]$$
(6s - 5)^2.
$$[/tex]
