Write the expanded form of (5a + 7b + 3c)².
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A.
25a² + 49b² + 9c² + 70ab + 37bc + 30ac
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B.
25a² + 49b² + 9c² + 70ab + 42bc + 30ac
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C.
25a² + 49b² + 9c² + 74ab + 42bc + 30ac
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D.
25a² + 49b² + 9c² + 70ab + 42bc + 40ac
Correct Answer:
B. 25a² + 49b² + 9c² + 70ab + 42bc + 30ac
Explanation:
To expand the expression (5a + 7b + 3c)^2, apply the algebraic identity (x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx. Substituting the given terms: (5a)^2 + (7b)^2 + (3c)^2 + 2(5a)(7b) + 2(7b)(3c) + 2(3c)(5a). This simplifies to 25a^2 + 49b^2 + 9c^2 + 70ab + 42bc + 30ac.
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