What is expand (2y^4-1)^6 ?

The solution to expand (2y^4-1)^6 is 64y^{24}-192y^{20}+240y^{16}-160y^{12}+60y^8-12y^4+1

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expand (2y^4-1)^6

expand

(2 y^{4} - 1)^{6}

64 y^{24} - 192 y^{20} + 240 y^{16} - 160 y^{12} + 60 y^{8} - 12 y^{4} + 1

Solution steps

(2 y^{4} - 1)^{6}

Apply binomial theorem:

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

a = 2 y^{4}, b = - 1

= i = 0 \sum 6 (i 6) (2 y^{4})^{(6 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (2 y^{4})^{6} (- 1)^{0} : 64 y^{24}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (2 y^{4})^{5} (- 1)^{1} : - 192 y^{20}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (2 y^{4})^{4} (- 1)^{2} : 240 y^{16}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (2 y^{4})^{3} (- 1)^{3} : - 160 y^{12}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (2 y^{4})^{2} (- 1)^{4} : 60 y^{8}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (2 y^{4})^{1} (- 1)^{5} : - 12 y^{4}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (2 y^{4})^{0} (- 1)^{6} : 1

= 64 y^{24} - 192 y^{20} + 240 y^{16} - 160 y^{12} + 60 y^{8} - 12 y^{4} + 1

\frac{( 8 m ^{2} - 2 )}{( 2 m ^{2} )}

3 a^{5} b - a^{3} c

- 4 y - 3

l^{- 1} \cdot (\frac{3}{( s ^{5} )})

(\frac{3}{2})^{x} (\frac{2}{3})^{x}

What is expand (2y^4-1)^6 ?
The solution to expand (2y^4-1)^6 is 64y^{24}-192y^{20}+240y^{16}-160y^{12}+60y^8-12y^4+1