How do you expand ${(1 + 4 x^{4})}^{4}$ $(1+4x^4)^4$ ?

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Answer 1 · 2017-12-10T12:38:32

${(1 + 4 x^{4})}^{4} = 1 + 16 x^{4} + 96 x^{8} + 256 x^{12} + 256 x^{16} .$ $(1+4x^4)^4=1+16x^4+96x^8 +256x^12+256x^16 .$

$(a + b)^n =(nC_0) a^nb^0+ (nC_1) a^(n-1)b^1 +(nC_2) a^(n-2)b^2 +...... (nC_n)b^n$

Here $(a=1 ; b=4x^4 , n= 4) :. 1^n=1 , x^0=1$

We know $nC_r= (n!)/(r!(n-r)!)$

$:. 4C_0=1 , 4C_1=4 , 4C_2=6 ,4C_3=4,4C_4=1$

$:. (1+x)^3= 1 + 3x+3x^2+x^3 :.$

$(1+4x^4)^4 = 1^4 + 4*1^3*4x^4+6*1^2*(4x^4)^2+4*1* (4x^4)^3 + (4x^4)^4$

$:. (1+4x^4)^4=1+16x^4+96x^8 +256x^12+256x^16$
[Ans]

How do you expand (1+4x^4)^4(1+4x4)4(1+4x^4)^4?