Write the expanded form of (3a + 6b + 5c)².
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A.
9a² + 36b² + 25c² + 40ab + 60bc + 30ac
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B.
9a² + 36b² + 25c² + 36ab + 60bc + 30ac
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C.
9a² + 36b² + 25c² + 36ab + 60bc + 40ac
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D.
9a² + 36b² + 25c² + 36ab + 55bc + 30ac
Correct Answer:
B. 9a² + 36b² + 25c² + 36ab + 60bc + 30ac
Explanation:
The correct answer is Option B: 9a2 + 36b2 + 25c2 + 36ab + 60bc + 30ac.
To expand the expression (3a + 6b + 5c)2, we use the algebraic identity (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx. Substituting x = 3a, y = 6b, and z = 5c into the formula, we get (3a)2 + (6b)2 + (5c)2 + 2(3a)(6b) + 2(6b)(5c) + 2(5c)(3a). Squaring the individual terms gives 9a2 + 36b2 + 25c2. Multiplying the cross-product terms results in 36ab, 60bc, and 30ac. Combining all these parts yields the final expanded form: 9a2 + 36b2 + 25c2 + 36ab + 60bc + 30ac.
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