To simplify the expression (121 - 22c + c^2), we can rearrange it in standard quadratic form. The expression can be rewritten as:
[ c^2 - 22c + 121 ]
This is a quadratic expression in terms of (c). If you're looking to solve for (c) by factoring or using the quadratic formula, let's check if it can be factored first.
To factor (c^2 - 22c + 121), we look for two numbers that multiply to (121) (the constant term) and add to (-22) (the coefficient of (c)).
The numbers (-11) and (-11) satisfy this condition since:
[
-11 \times -11 = 121 \quad \text{and} \quad -11 - 11 = -22
]
Thus, we can factor the expression as:
[
(c - 11)(c - 11) \quad \text{or} \quad (c - 11)^2
]
So, the simplified form of the expression (121 - 22c + c^2) is:
[
(c - 11)^2
]
If you need to solve for (c), set the expression equal to zero:
[
(c - 11)^2 = 0
]
This gives:
[
c - 11 = 0 \quad \Rightarrow \quad c = 11
]
Thus, (c = 11) is the only solution.
