Let's solve the given quadratic expression [tex]\( b^2 - 26b + 144 \)[/tex].
### Step 1: Write the quadratic expression
We start with:
[tex]\[ b^2 - 26b + 144 \][/tex]
### Step 2: Simplify the expression
In this case, the expression is already simplified as there are no like terms to combine.
### Step 3: Factor the quadratic expression
To factorize the quadratic expression [tex]\( b^2 - 26b + 144 \)[/tex], we need to find two numbers that multiply to give the constant term ([tex]\( 144 \)[/tex]) and add to give the coefficient of the [tex]\( b \)[/tex] term ([tex]\( -26 \)[/tex]).
We look for two numbers [tex]\( m \)[/tex] and [tex]\( n \)[/tex] such that:
[tex]\[ m \cdot n = 144 \][/tex]
[tex]\[ m + n = -26 \][/tex]
After examining possible pairs, we find:
[tex]\[ m = -18 \][/tex]
[tex]\[ n = -8 \][/tex]
Because:
[tex]\[ (-18) \cdot (-8) = 144 \][/tex]
[tex]\[ (-18) + (-8) = -26 \][/tex]
### Step 4: Write the factors of the quadratic expression
Given the numbers [tex]\( -18 \)[/tex] and [tex]\( -8 \)[/tex], we can write the factorized form of the quadratic expression as:
[tex]\[ b^2 - 26b + 144 = (b - 18)(b - 8) \][/tex]
### Summary
The quadratic expression [tex]\( b^2 - 26b + 144 \)[/tex] can be factorized as:
[tex]\[ (b - 18)(b - 8) \][/tex]
Thus, the simplified expression and its factorized form are:
[tex]\[ b^2 - 26b + 144 \][/tex]
[tex]\[ (b - 18)(b - 8) \][/tex]
