Write the expanded form of (3a + 5b + 7c)².
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A.
9a² + 25b² + 49c² + 30ab + 70bc + 52ac
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B.
9a² + 25b² + 49c² + 30ab + 70bc + 42ac
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C.
9a² + 25b² + 49c² + 30ab + 65bc + 42ac
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D.
9a² + 25b² + 49c² + 34ab + 70bc + 42ac
Correct Answer:
B. 9a² + 25b² + 49c² + 30ab + 70bc + 42ac
Explanation:
The correct answer is Option B: 9a2 + 25b2 + 49c2 + 30ab + 70bc + 42ac.
To expand the algebraic expression (3a + 5b + 7c)2, we use the identity (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx. By substituting x = 3a, y = 5b, and z = 7c, we first square each term to get 9a2, 25b2, and 49c2. Next, we calculate the product of each pair of terms and multiply by two: 2(3a)(5b) results in 30ab, 2(5b)(7c) results in 70bc, and 2(3a)(7c) results in 42ac. Combining all these components yields the final expanded form: 9a2 + 25b2 + 49c2 + 30ab + 70bc + 42ac.
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