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Stolb23 [73]
3 years ago
9

1. What is the fourth term in the expansion of (x + 4y)^6?

Mathematics
1 answer:
aev [14]3 years ago
7 0
For the fourth term r = 3
Fourth term = 6C3(x)^(6 - 3) (4y)^3 = 20x^3 (64y^3) = 1,280x^3y^3
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Answer:

The third option listed: \sqrt[3]{2x} -6\sqrt[3]{x}\\

Step-by-step explanation:

We start by writing all the numerical factors inside the qubic roots in factor form (and if possible with exponent 3 so as to easily identify what can be extracted from the root):

7\sqrt[3]{2x}  -3\sqrt[3]{16x} -3\sqrt[3]{8x} =\\=7\sqrt[3]{2x}  -3\sqrt[3]{2^32x} -3\sqrt[3]{2^3x} =\\=7\sqrt[3]{2x}  -3*2\sqrt[3]{2x} -3*2\sqrt[3]{x}=\\=7\sqrt[3]{2x}  -6\sqrt[3]{2x} -6\sqrt[3]{x}

And now we combine all like terms (notice that the only two terms we can combine are the first two, which contain the exact same radical form:

7\sqrt[3]{2x}  -6\sqrt[3]{2x} -6\sqrt[3]{x}=\\=\sqrt[3]{2x} -6\sqrt[3]{x}

Therefore this is the simplified radical expression: \sqrt[3]{2x} -6\sqrt[3]{x}\\

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