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Popular >

expand 15(3/2+15/16 x)^6

Solution

expand

15 (\frac{3}{2} + \frac{15}{16} x)^{6}

Solution

\frac{10935}{64} + \frac{164025 x}{256} + \frac{4100625 x ^{2}}{4096} + \frac{6834375 x ^{3}}{8192} + \frac{102515625 x ^{4}}{262144} + \frac{102515625 x ^{5}}{1048576} + \frac{170859375 x ^{6}}{16777216}

Solution steps

15 (\frac{3}{2} + \frac{15}{16} x)^{6}

Expand

(\frac{3}{2} + \frac{15}{16} x)^{6} : \frac{729}{64} + \frac{10935 x}{256} + \frac{273375 x ^{2}}{4096} + \frac{455625 x ^{3}}{8192} + \frac{6834375 x ^{4}}{262144} + \frac{6834375 x ^{5}}{1048576} + \frac{11390625 x ^{6}}{16777216}

= 15 (\frac{729}{64} + \frac{10935 x}{256} + \frac{273375 x ^{2}}{4096} + \frac{455625 x ^{3}}{8192} + \frac{6834375 x ^{4}}{262144} + \frac{6834375 x ^{5}}{1048576} + \frac{11390625 x ^{6}}{16777216})

Distribute parentheses

= 15 \cdot \frac{729}{64} + 15 \cdot \frac{10935 x}{256} + 15 \cdot \frac{273375 x ^{2}}{4096} + 15 \cdot \frac{455625 x ^{3}}{8192} + 15 \cdot \frac{6834375 x ^{4}}{262144} + 15 \cdot \frac{6834375 x ^{5}}{1048576} + 15 \cdot \frac{11390625 x ^{6}}{16777216}

Simplify

15 \cdot \frac{729}{64} + 15 \cdot \frac{10935 x}{256} + 15 \cdot \frac{273375 x ^{2}}{4096} + 15 \cdot \frac{455625 x ^{3}}{8192} + 15 \cdot \frac{6834375 x ^{4}}{262144} + 15 \cdot \frac{6834375 x ^{5}}{1048576} + 15 \cdot \frac{11390625 x ^{6}}{16777216} : \frac{10935}{64} + \frac{164025 x}{256} + \frac{4100625 x ^{2}}{4096} + \frac{6834375 x ^{3}}{8192} + \frac{102515625 x ^{4}}{262144} + \frac{102515625 x ^{5}}{1048576} + \frac{170859375 x ^{6}}{16777216}

= \frac{10935}{64} + \frac{164025 x}{256} + \frac{4100625 x ^{2}}{4096} + \frac{6834375 x ^{3}}{8192} + \frac{102515625 x ^{4}}{262144} + \frac{102515625 x ^{5}}{1048576} + \frac{170859375 x ^{6}}{16777216}

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Frequently Asked Questions (FAQ)

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