Write the expanded form of (8a + 5b + 9c)².
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A.
64a² + 25b² + 81c² + 84ab + 90bc + 144ac
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B.
64a² + 25b² + 81c² + 80ab + 85bc + 144ac
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C.
64a² + 25b² + 81c² + 80ab + 90bc + 144ac
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D.
64a² + 25b² + 81c² + 80ab + 90bc + 154ac
Correct Answer:
C. 64a² + 25b² + 81c² + 80ab + 90bc + 144ac
Explanation:
To expand the expression (8a + 5b + 9c)^2, apply the algebraic identity for the square of a trinomial: (x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx. By substituting x = 8a, y = 5b, and z = 9c, the squares are 64a^2, 25b^2, and 81c^2. The product terms are 2(8a)(5b) = 80ab, 2(5b)(9c) = 90bc, and 2(8a)(9c) = 144ac. Combining these results yields the final expanded form: 64a^2 + 25b^2 + 81c^2 + 80ab + 90bc + 144ac.
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