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Popular >

expand ((3x-y)/3)^{14}

Solution

expand

(\frac{3 x - y}{3})^{14}

Solution

x^{14} - \frac{14 x ^{13} y}{3} + \frac{91 x ^{12} y ^{2}}{9} - \frac{364 x ^{11} y ^{3}}{27} + \frac{1001 x ^{10} y ^{4}}{81} - \frac{2002 x ^{9} y ^{5}}{243} + \frac{1001 x ^{8} y ^{6}}{243} - \frac{1144 x ^{7} y ^{7}}{729} + \frac{1001 x ^{6} y ^{8}}{2187} - \frac{2002 x ^{5} y ^{9}}{19683} + \frac{1001 x ^{4} y ^{10}}{59049} - \frac{364 x ^{3} y ^{11}}{177147} + \frac{91 x ^{2} y ^{12}}{531441} - \frac{14 x y ^{13}}{1594323} + \frac{y ^{14}}{4782969}

Solution steps

(\frac{3 x - y}{3})^{14}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 x - y ) ^{14}}{3 ^{14}}

(3 x - y)^{14} = 4782969 x^{14} - 22320522 x^{13} y + 48361131 x^{12} y^{2} - 64481508 x^{11} y^{3} + 59108049 x^{10} y^{4} - 39405366 x^{9} y^{5} + 19702683 x^{8} y^{6} - 7505784 x^{7} y^{7} + 2189187 x^{6} y^{8} - 486486 x^{5} y^{9} + 81081 x^{4} y^{10} - 9828 x^{3} y^{11} + 819 x^{2} y^{12} - 42 x y^{13} + y^{14}

= \frac{4782969 x ^{14} - 22320522 x ^{13} y + 48361131 x ^{12} y ^{2} - 64481508 x ^{11} y ^{3} + 59108049 x ^{10} y ^{4} - 39405366 x ^{9} y ^{5} + 19702683 x ^{8} y ^{6} - 7505784 x ^{7} y ^{7} + 2189187 x ^{6} y ^{8} - 486486 x ^{5} y ^{9} + 81081 x ^{4} y ^{10} - 9828 x ^{3} y ^{11} + 819 x ^{2} y ^{12} - 42 x y ^{13} + y ^{14}}{3 ^{14}}

3^{14} = 4782969

= \frac{4782969 x ^{14} - 22320522 x ^{13} y + 48361131 x ^{12} y ^{2} - 64481508 x ^{11} y ^{3} + 59108049 x ^{10} y ^{4} - 39405366 x ^{9} y ^{5} + 19702683 x ^{8} y ^{6} - 7505784 x ^{7} y ^{7} + 2189187 x ^{6} y ^{8} - 486486 x ^{5} y ^{9} + 81081 x ^{4} y ^{10} - 9828 x ^{3} y ^{11} + 819 x ^{2} y ^{12} - 42 x y ^{13} + y ^{14}}{4782969}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{4782969 x ^{14} - 22320522 x ^{13} y + 48361131 x ^{12} y ^{2} - 64481508 x ^{11} y ^{3} + 59108049 x ^{10} y ^{4} - 39405366 x ^{9} y ^{5} + 19702683 x ^{8} y ^{6} - 7505784 x ^{7} y ^{7} + 2189187 x ^{6} y ^{8} - 486486 x ^{5} y ^{9} + 81081 x ^{4} y ^{10} - 9828 x ^{3} y ^{11} + 819 x ^{2} y ^{12} - 42 x y ^{13} + y ^{14}}{4782969} = \frac{4782969 x ^{14}}{4782969} - \frac{22320522 x ^{13} y}{4782969} + \frac{48361131 x ^{12} y ^{2}}{4782969} - \frac{64481508 x ^{11} y ^{3}}{4782969} + \frac{59108049 x ^{10} y ^{4}}{4782969} - \frac{39405366 x ^{9} y ^{5}}{4782969} + \frac{19702683 x ^{8} y ^{6}}{4782969} - \frac{7505784 x ^{7} y ^{7}}{4782969} + \frac{2189187 x ^{6} y ^{8}}{4782969} - \frac{486486 x ^{5} y ^{9}}{4782969} + \frac{81081 x ^{4} y ^{10}}{4782969} - \frac{9828 x ^{3} y ^{11}}{4782969} + \frac{819 x ^{2} y ^{12}}{4782969} - \frac{42 x y ^{13}}{4782969} + \frac{y ^{14}}{4782969}

= \frac{4782969 x ^{14}}{4782969} - \frac{22320522 x ^{13} y}{4782969} + \frac{48361131 x ^{12} y ^{2}}{4782969} - \frac{64481508 x ^{11} y ^{3}}{4782969} + \frac{59108049 x ^{10} y ^{4}}{4782969} - \frac{39405366 x ^{9} y ^{5}}{4782969} + \frac{19702683 x ^{8} y ^{6}}{4782969} - \frac{7505784 x ^{7} y ^{7}}{4782969} + \frac{2189187 x ^{6} y ^{8}}{4782969} - \frac{486486 x ^{5} y ^{9}}{4782969} + \frac{81081 x ^{4} y ^{10}}{4782969} - \frac{9828 x ^{3} y ^{11}}{4782969} + \frac{819 x ^{2} y ^{12}}{4782969} - \frac{42 x y ^{13}}{4782969} + \frac{y ^{14}}{4782969}

\frac{4782969 x ^{14}}{4782969} = x^{14}

\frac{22320522 x ^{13} y}{4782969} = \frac{14 x ^{13} y}{3}

\frac{48361131 x ^{12} y ^{2}}{4782969} = \frac{91 x ^{12} y ^{2}}{9}

\frac{64481508 x ^{11} y ^{3}}{4782969} = \frac{364 x ^{11} y ^{3}}{27}

\frac{59108049 x ^{10} y ^{4}}{4782969} = \frac{1001 x ^{10} y ^{4}}{81}

\frac{39405366 x ^{9} y ^{5}}{4782969} = \frac{2002 x ^{9} y ^{5}}{243}

\frac{19702683 x ^{8} y ^{6}}{4782969} = \frac{1001 x ^{8} y ^{6}}{243}

\frac{7505784 x ^{7} y ^{7}}{4782969} = \frac{1144 x ^{7} y ^{7}}{729}

\frac{2189187 x ^{6} y ^{8}}{4782969} = \frac{1001 x ^{6} y ^{8}}{2187}

\frac{486486 x ^{5} y ^{9}}{4782969} = \frac{2002 x ^{5} y ^{9}}{19683}

\frac{81081 x ^{4} y ^{10}}{4782969} = \frac{1001 x ^{4} y ^{10}}{59049}

\frac{9828 x ^{3} y ^{11}}{4782969} = \frac{364 x ^{3} y ^{11}}{177147}

\frac{819 x ^{2} y ^{12}}{4782969} = \frac{91 x ^{2} y ^{12}}{531441}

\frac{42 x y ^{13}}{4782969} = \frac{14 x y ^{13}}{1594323}

= x^{14} - \frac{14 x ^{13} y}{3} + \frac{91 x ^{12} y ^{2}}{9} - \frac{364 x ^{11} y ^{3}}{27} + \frac{1001 x ^{10} y ^{4}}{81} - \frac{2002 x ^{9} y ^{5}}{243} + \frac{1001 x ^{8} y ^{6}}{243} - \frac{1144 x ^{7} y ^{7}}{729} + \frac{1001 x ^{6} y ^{8}}{2187} - \frac{2002 x ^{5} y ^{9}}{19683} + \frac{1001 x ^{4} y ^{10}}{59049} - \frac{364 x ^{3} y ^{11}}{177147} + \frac{91 x ^{2} y ^{12}}{531441} - \frac{14 x y ^{13}}{1594323} + \frac{y ^{14}}{4782969}

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