Korzystamy z wzoru:

$a^n+b^n=\left(a+b\right)\left(a^{n-1}-a^{n-2}\cdot b+a^{n-3}\cdot b^2-\dots +a^2{b}^{n-3}-a{b}^{n-2}+b^{n-1}\right)$  

zatem:   


$a\text{)}{4}^5+1=4^5+1^5=\left(4+1\right)\left(4^4-4^3\cdot 1+4^2\cdot 1^2-4\cdot 1^3+1^4\right)=\left(4+1\right)\left(4^4-4^3+4^2-4+1\right)$  

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$b\text{)}\frac{1}{128}{a}^7+{\left(bc\right)}^7={\left(\frac{1}{2}a\right)}^7+{\left(bc\right)}^7=\left(\frac{1}{2}a+bc\right)\left({\left(\frac{1}{2}a\right)}^6-{\left(\frac{1}{2}a\right)}^5\cdot bc+{\left(\frac{1}{2}a\right)}^4\cdot {\left(bc\right)}^2-{\left(\frac{1}{2}a\right)}^3\cdot {\left(bc\right)}^3+{\left(\frac{1}{2}a\right)}^2\cdot {\left(bc\right)}^4-\frac{1}{2}a\cdot {\left(bc\right)}^5+{\left(bc\right)}^6\right)$