Which of the following is an example of the associative property of addition?

a + (b + c) = a b + a c

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a + (b + c) = b (a + c)

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a + (b + c) = (a + b) + c

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a \times (b + c) = a b + a c

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Solution

The correct option is C $a + (b + c) = (a + b) + c$
The associative property states that you can add or multiply regardless of how the numbers are grouped.

Therefore, $a + (b + c) = (a + b) + c$ is an example of the associative property of addition.

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\frac{a^{3} (b + c)}{(a - b) (a - c)} + \frac{b^{3} (c + a)}{(b - c) (b - a)} + \frac{a^{3} (a + b)}{(c - a) (c - b)} = b c + c a + a b

⎡ ⎢ ⎣ \begin{matrix} a & a^{2} & b c b & b^{2} & c a c & c^{2} & a b \end{matrix} ⎤ ⎥ ⎦

= (a - b) (b - c) (c - a) (b c + c a + a b)

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + a b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3. (b - c) (c - a) (a - b) (a + b + c) (a b + b c + c a)

a, b,

c

(a b + b c) (- c b + b a) + (b c + c a) (- a c + c b) + (c a + a b) (a c - b a)

{tan}^{- 1} \sqrt{\frac{a (a + b + c)}{b c}} + {tan}^{- 1} \sqrt{\frac{b (a + b + c)}{c a}} + {tan}^{- 1} \sqrt{\frac{c (a + b + c)}{a b}}

a, b, c > 0

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