Multiply the algebraic expression using a Special Product Formula, and simplify. (2+y3)2

Step 1
Given:
${\displaystyle {(2+y^3)}^2}$
Step 2
${\displaystyle {(2+y^3)}^2=4+y^6+4y^3}$
${\displaystyle =4+{\left(y^2\right)}^3+4y^3}$
${\displaystyle =4+(y^2+4y)(y^4-4y^3+16y^2)}$

The square of a binomial.
The square of a binomial sum is first term square plus two times the product of the sums plus last term square. Here we use the FOIL method.
FOIL Method:
FOIL is a standard method of multiplying two binomials. The word is the acronym for the four terms of the product.
Given expression is ${\displaystyle ={(2+y^3)}^2}$
Square of a given binomial sum
${\displaystyle {(2+y^3)}^2={\left(2\right)}^2+2\cdot 2\cdot y^3+{\left(y^3\right)}^2}$
First 2 times second ${\displaystyle term+the\prod uct+term}$ squared of 2 terms squared
${\displaystyle =4+4y^3+y^6}$ (by using square of binomial formula)

$(2+y^3{)}^2$
$(2+y^3{)}^2=4+y^6+4y^3$
$=4+(y^2{)}^3+4y^3$
$=4+(y^2+4y)(y^4-4y^3+16y^2)$