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Popular >

expand (5a-3/b)^7

Solution

expand

(5 a - \frac{3}{b})^{7}

Solution

78125 a^{7} - \frac{328125 a ^{6}}{b} + \frac{590625 a ^{5}}{b ^{2}} - \frac{590625 a ^{4}}{b ^{3}} + \frac{354375 a ^{3}}{b ^{4}} - \frac{127575 a ^{2}}{b ^{5}} + \frac{25515 a}{b ^{6}} - \frac{2187}{b ^{7}}

Solution steps

(5 a - \frac{3}{b})^{7}

Apply binomial theorem:

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

a = 5 a, b = - \frac{3}{b}

= i = 0 \sum 7 (i 7) (5 a)^{(7 - i)} (- \frac{3}{b})^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} (5 a)^{7} (- \frac{3}{b})^{0} : 78125 a^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} (5 a)^{6} (- \frac{3}{b})^{1} : - \frac{328125 a ^{6}}{b}

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} (5 a)^{5} (- \frac{3}{b})^{2} : \frac{590625 a ^{5}}{b ^{2}}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} (5 a)^{4} (- \frac{3}{b})^{3} : - \frac{590625 a ^{4}}{b ^{3}}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} (5 a)^{3} (- \frac{3}{b})^{4} : \frac{354375 a ^{3}}{b ^{4}}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} (5 a)^{2} (- \frac{3}{b})^{5} : - \frac{127575 a ^{2}}{b ^{5}}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} (5 a)^{1} (- \frac{3}{b})^{6} : \frac{25515 a}{b ^{6}}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} (5 a)^{0} (- \frac{3}{b})^{7} : - \frac{2187}{b ^{7}}

= 78125 a^{7} - \frac{328125 a ^{6}}{b} + \frac{590625 a ^{5}}{b ^{2}} - \frac{590625 a ^{4}}{b ^{3}} + \frac{354375 a ^{3}}{b ^{4}} - \frac{127575 a ^{2}}{b ^{5}} + \frac{25515 a}{b ^{6}} - \frac{2187}{b ^{7}}

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Frequently Asked Questions (FAQ)

What is expand (5a-3/b)^7 ?
The solution to expand (5a-3/b)^7 is