Write the expanded form of (4a + 6b + 9c)².
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A.
16a²+36b²+81c²+48ab+103bc+72ac
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B.
16a² + 36b² + 81c² + 48ab + 108bc + 82ac
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C.
16a² + 36b² + 81c² + 52ab + 108bc + 72ac
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D.
16a² + 36b² + 81c² + 48ab + 108bc + 72ac
Correct Answer:
D. 16a² + 36b² + 81c² + 48ab + 108bc + 72ac
Explanation:
The correct answer is Option D: 16a2 + 36b2 + 81c2 + 48ab + 108bc + 72ac.
To expand the expression (4a + 6b + 9c)2, we use the algebraic identity (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx. In this problem, x = 4a, y = 6b, and z = 9c.
First, square each individual term: (4a)2 = 16a2, (6b)2 = 36b2, and (9c)2 = 81c2.
Next, calculate the product of each pair of terms and multiply by two: - 2(4a)(6b) = 48ab
- 2(6b)(9c) = 108bc
- 2(9c)(4a) = 72acCombining all these components gives the final expanded form: 16a2 + 36b2 + 81c2 + 48ab + 108bc + 72ac.
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