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Popular >

expand (1/(p^2)-4q)^7

Solution

expand

(\frac{1}{p ^{2}} - 4 q)^{7}

Solution

\frac{1}{p ^{14}} - \frac{28 q}{p ^{12}} + \frac{336 q ^{2}}{p ^{10}} - \frac{2240 q ^{3}}{p ^{8}} + \frac{8960 q ^{4}}{p ^{6}} - \frac{21504 q ^{5}}{p ^{4}} + \frac{28672 q ^{6}}{p ^{2}} - 16384 q^{7}

Solution steps

(\frac{1}{p ^{2}} - 4 q)^{7}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = \frac{1}{p ^{2}}, b = - 4 q

= i = 0 \sum 7 (i 7) (\frac{1}{p ^{2}})^{(7 - i)} (- 4 q)^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} (\frac{1}{p ^{2}})^{7} (- 4 q)^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} (\frac{1}{p ^{2}})^{6} (- 4 q)^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} (\frac{1}{p ^{2}})^{5} (- 4 q)^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} (\frac{1}{p ^{2}})^{4} (- 4 q)^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} (\frac{1}{p ^{2}})^{3} (- 4 q)^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} (\frac{1}{p ^{2}})^{2} (- 4 q)^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} (\frac{1}{p ^{2}})^{1} (- 4 q)^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} (\frac{1}{p ^{2}})^{0} (- 4 q)^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} (\frac{1}{p ^{2}})^{7} (- 4 q)^{0} : \frac{1}{p ^{14}}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} (\frac{1}{p ^{2}})^{6} (- 4 q)^{1} : - \frac{28 q}{p ^{12}}

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} (\frac{1}{p ^{2}})^{5} (- 4 q)^{2} : \frac{336 q ^{2}}{p ^{10}}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} (\frac{1}{p ^{2}})^{4} (- 4 q)^{3} : - \frac{2240 q ^{3}}{p ^{8}}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} (\frac{1}{p ^{2}})^{3} (- 4 q)^{4} : \frac{8960 q ^{4}}{p ^{6}}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} (\frac{1}{p ^{2}})^{2} (- 4 q)^{5} : - \frac{21504 q ^{5}}{p ^{4}}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} (\frac{1}{p ^{2}})^{1} (- 4 q)^{6} : \frac{28672 q ^{6}}{p ^{2}}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} (\frac{1}{p ^{2}})^{0} (- 4 q)^{7} : - 16384 q^{7}

= \frac{1}{p ^{14}} - \frac{28 q}{p ^{12}} + \frac{336 q ^{2}}{p ^{10}} - \frac{2240 q ^{3}}{p ^{8}} + \frac{8960 q ^{4}}{p ^{6}} - \frac{21504 q ^{5}}{p ^{4}} + \frac{28672 q ^{6}}{p ^{2}} - 16384 q^{7}

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Frequently Asked Questions (FAQ)

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