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Popular >

expand (1-3/4 x)^8

Solution

expand

(1 - \frac{3}{4} x)^{8}

Solution

1 - 6 x + \frac{63 x ^{2}}{4} - \frac{189 x ^{3}}{8} + \frac{2835 x ^{4}}{128} - \frac{1701 x ^{5}}{128} + \frac{5103 x ^{6}}{1024} - \frac{2187 x ^{7}}{2048} + \frac{6561 x ^{8}}{65536}

Solution steps

(1 - \frac{3}{4} x)^{8}

Apply binomial theorem:

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

a = 1, b = - \frac{3}{4} x

= i = 0 \sum 8 (i 8) \cdot 1^{(8 - i)} (- \frac{3}{4} x)^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 1^{8} (- \frac{3}{4} x)^{0} : 1

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 1^{7} (- \frac{3}{4} x)^{1} : - 6 x

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 1^{6} (- \frac{3}{4} x)^{2} : \frac{63 x ^{2}}{4}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 1^{5} (- \frac{3}{4} x)^{3} : - \frac{189 x ^{3}}{8}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 1^{4} (- \frac{3}{4} x)^{4} : \frac{2835 x ^{4}}{128}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 1^{3} (- \frac{3}{4} x)^{5} : - \frac{1701 x ^{5}}{128}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 1^{2} (- \frac{3}{4} x)^{6} : \frac{5103 x ^{6}}{1024}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 1^{1} (- \frac{3}{4} x)^{7} : - \frac{2187 x ^{7}}{2048}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 1^{0} (- \frac{3}{4} x)^{8} : \frac{6561 x ^{8}}{65536}

= 1 - 6 x + \frac{63 x ^{2}}{4} - \frac{189 x ^{3}}{8} + \frac{2835 x ^{4}}{128} - \frac{1701 x ^{5}}{128} + \frac{5103 x ^{6}}{1024} - \frac{2187 x ^{7}}{2048} + \frac{6561 x ^{8}}{65536}

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Frequently Asked Questions (FAQ)

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