Question

Simplify (y + 1)^5y + 1)^3​

Answer 1

Note: Your expression sounds a little unclear, so I am assuming your expression is

$\left(y\:+\:1\right)^5\times \left(y\:+\:1\right)^3$

But, the procedure to solve the expressions involving exponents remains the same, so whatever the expression is, you may be able to get your concept clear.

In the end, I will solve both expressions.

Answer:

Please check the explanation

Step-by-step explanation:

Given the expression

$\left(y\:+\:1\right)^5\times \left(y\:+\:1\right)^3$

solving the expression

$\left(y\:+\:1\right)^5\times \left(y\:+\:1\right)^3$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}$

$\left(y+1\right)^5\left(y+1\right)^3=\left(y+1\right)^{5+3}$

                          $=\left(y+1\right)^8$

Therefore, we conclude that:

$\left(y\:+\:1\right)^5\times \left(y\:+\:1\right)^3=\left(y+1\right)^8$

IF YOUR EXPRESSION IS THIS

                       ↓

$\left(y\:+\:1\right)^{\left(5y+1\right)^3}$

solving the expression

as

$\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3$

so

$\left(5y+1\right)^3=125y^3+75y^2+15y+1$

               $=125y^3+75y^2+15y+1$

Thus, the expression becomes

$\left(y+1\right)^{\left(5y+1\right)^3}=\left(y+1\right)^{125y^3+75y^2+15y+1}$