Simplify the expression b(y)=(y^(-1)+y^(-2))(2y^(-3)-8y^(-4))

 Exercise

$b\left(y\right)=\left(y^{-1}+y^{-2}\right)\left(2y^{-3}-8y^{-4}\right)$

 

Multiplying polynomials $y^{-1}+y^{-2}$ and $2y^{-3}-8y^{-4}$

$b\left(y\right)=2\left(y^{-1}+y^{-2}\right)y^{-3}-8\left(y^{-1}+y^{-2}\right)y^{-4}$

 

Multiply the single term $2y^{-3}$ by each term of the polynomial $\left(y^{-1}+y^{-2}\right)$

$b\left(y\right)=2y^{-4}+2y^{-5}-8\left(y^{-1}+y^{-2}\right)y^{-4}$

 

Multiply the single term $-8y^{-4}$ by each term of the polynomial $\left(y^{-1}+y^{-2}\right)$

$b\left(y\right)=2y^{-4}+2y^{-5}-8y^{-5}-8y^{-6}$

 

Combining like terms $2y^{-5}$ and $-8y^{-5}$

$b\left(y\right)=2y^{-4}-6y^{-5}-8y^{-6}$

$b\left(y\right)=2y^{-4}-6y^{-5}-8y^{-6}$

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