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Popular >

expand (5a+3b)^9

Solution

expand

(5 a + 3 b)^{9}

Solution

1953125 a^{9} + 10546875 a^{8} b + 25312500 a^{7} b^{2} + 35437500 a^{6} b^{3} + 31893750 a^{5} b^{4} + 19136250 a^{4} b^{5} + 7654500 a^{3} b^{6} + 1968300 a^{2} b^{7} + 295245 a b^{8} + 19683 b^{9}

Solution steps

(5 a + 3 b)^{9}

Apply binomial theorem:

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

a = 5 a, b = 3 b

= i = 0 \sum 9 (i 9) (5 a)^{(9 - i)} (3 b)^{i}

Expand summation

= \frac{9 !}{0 ! ( 9 - 0 ) !} (5 a)^{9} (3 b)^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} (5 a)^{8} (3 b)^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} (5 a)^{7} (3 b)^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} (5 a)^{6} (3 b)^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} (5 a)^{5} (3 b)^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} (5 a)^{4} (3 b)^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} (5 a)^{3} (3 b)^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} (5 a)^{2} (3 b)^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} (5 a)^{1} (3 b)^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} (5 a)^{0} (3 b)^{9}

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} (5 a)^{9} (3 b)^{0} : 1953125 a^{9}

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} (5 a)^{8} (3 b)^{1} : 10546875 a^{8} b

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} (5 a)^{7} (3 b)^{2} : 25312500 a^{7} b^{2}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} (5 a)^{6} (3 b)^{3} : 35437500 a^{6} b^{3}

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} (5 a)^{5} (3 b)^{4} : 31893750 a^{5} b^{4}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} (5 a)^{4} (3 b)^{5} : 19136250 a^{4} b^{5}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} (5 a)^{3} (3 b)^{6} : 7654500 a^{3} b^{6}

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} (5 a)^{2} (3 b)^{7} : 1968300 a^{2} b^{7}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} (5 a)^{1} (3 b)^{8} : 295245 a b^{8}

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} (5 a)^{0} (3 b)^{9} : 19683 b^{9}

= 1953125 a^{9} + 10546875 a^{8} b + 25312500 a^{7} b^{2} + 35437500 a^{6} b^{3} + 31893750 a^{5} b^{4} + 19136250 a^{4} b^{5} + 7654500 a^{3} b^{6} + 1968300 a^{2} b^{7} + 295245 a b^{8} + 19683 b^{9}

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Frequently Asked Questions (FAQ)

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