Which example illustrates the associative property of addition for polynomials? [(2x2 + 5x) + (4x2 – 4x)] + 5x3 = (2x2 + 5x) + [(4x2 – 4x) + 5x3] [(2x2 + 5x) + (4x2 – 4x)] + 5x3 = [(4x2 – 4x) + (2x2 + 5x)] + 5x3 (2x2 + 5x) + [(4x2 – 4x) + 5x3] = (2x2 + 5x) + [5x3 + (4x2 – 4x)] [(2x2 + 5x) + (4x2 – 4x)] + 5x3 = [(5x + 2x2) + (–4x + 4x2)] + 5x3?

[(2x^2 + 5x) + (4x^2 – 4x)] + 5x^3 = (2x^2 + 5x) + [(4x^2 – 4x) + 5x^3]

Step-by-step explanation:

The associative property of addition states: (A +B) + C = A + (B + C).  That means, it doesn't matter which addition you make first, the final result remains the same. In this problem, A = (2x^2 + 5x), B = (4x^2 – 4x) and C = 5x^3. So, adding A to B and its result to C is the same as adding B to C and its result to A.

Option A; ((2x² + 5x) + (4x² – 4x)) + 5x³ = (2x² + 5x) + ((4x² – 4x)) + 5x³)

To answer this question, we need to know the meaning of associative property of addition.

       This property states that if the order of addition is changed, it will still yield the same result.

For example; (P + Q) + R must be equal to P + (Q + R).  

       ((2x² + 5x) + (4x² – 4x)) + 5x³ = (2x² + 5x) + ((4x² – 4x)) + 5x³)

Looking at the options, the one that corresponds to this answer is Option A

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