Given the polynomial expression:
(y + 5)²
(y - 5)(y + 5)
Let's simplify each of the given expression:
a.) (y + 5)²
The given equation is a factor of a perfect square trinomial. For this type of expression, the following is the formula for expanding it.
[tex]\text{ (a+b)}^2\text{ = }a^2\text{ + 2ab + }b^2[/tex]
We get,
[tex]\mleft(y+5\mright)^2=(y)^2+2(y)(5)+(5)^2[/tex][tex](y+5)^2=y^2+10y+25[/tex]
b.) (y - 5)(y + 5)
To be able to simplify the following expression. We will be using the formula for the difference of two squares.
[tex](a+b)(a-b)=a^2-b^2[/tex]
We get,
[tex]\mleft(y-5\mright)\mleft(y+5\mright)=(y)^2-(5)^2[/tex][tex](y-5)(y+5)=y^2-25^{}[/tex]
