Write the expanded form of (6a + 5b + 8c)².
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A.
36a² + 25b² + 64c² + 60ab + 80bc + 96ac
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B.
36a² + 25b² + 64c² + 60ab + 80bc + 106ac
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C.
36a² + 25b² + 64c² + 64ab + 80bc + 96ac
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D.
36a² + 25b² + 64c² + 60ab + 75bc + 96ac
Correct Answer:
A. 36a² + 25b² + 64c² + 60ab + 80bc + 96ac
Explanation:
To expand the expression (6a + 5b + 8c)2, apply the algebraic identity (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx. By substituting x = 6a, y = 5b, and z = 8c, the square of each term results in 36a2, 25b2, and 64c2, while the doubled products of the terms are 60ab, 80bc, and 96ac. Combining all these parts gives the final expanded form of 36a2 + 25b2 + 64c2 + 60ab + 80bc + 96ac.
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