Multiply. [c+1/5][c+1/5]=c^2+2c/5+1/25
Simplify the answer, is this correct
To simplify the expression, we need to simplify the terms individually and combine like terms. Let's go step by step:
Given expression: (c + 1/5)(c + 1/5)
To simplify, we can expand the expression using the distributive property:
(c + 1/5)(c + 1/5) = c(c) + c(1/5) + (1/5)(c) + (1/5)(1/5)
Now, let's multiply out each term:
c(c) = c^2
c(1/5) = c/5
(1/5)(c) = c/5
(1/5)(1/5) = 1/25
Combining like terms:
c^2 + c/5 + c/5 + 1/25
To simplify the fractions, we need to find a common denominator for c/5 and 1/25. The least common denominator (LCD) is 25:
c^2 + (5c/25) + (5c/25) + 1/25
Now, we can combine the fractions:
c^2 + (10c/25) + 1/25
Next, simplify the terms with the common denominator:
c^2 + (10c + 1)/25
Therefore, the simplified expression is:
c^2 + (10c + 1)/25
Yes, the expression c^2 + (10c + 1)/25 is the correct simplified form of (c + 1/5)(c + 1/5).