Answer:
y+yz is: [tex]2x^2-2x-1[/tex]
Step-by-step explanation:
Given expressions are:
[tex]y = x+\frac{1}{2}\\z = 2x-3[/tex]
The given expressions are polynomials and we have to find the value of y+yz
First of all, we will find the product of y and z
We will use the distribution to find the product.
[tex]yz = (x+\frac{1}{2})(2x-3)\\= x(2x-3)+\frac{1}{2}(2x-3)\\= 2x^2-3x+x-\frac{3}{2}\\=2x^2-2x- \frac{3}{2}[/tex]
The next step is to add y and yz
[tex]y+yz = (x+\frac{1}{2})+(2x^2-3x-\frac{3}{2})\\Combining\ like\ terms\\= 2x^2+x-3x+\frac{1}{2} -\frac{3}{2}\\=2x^2-2x + \frac{1-3}{2}\\=2x^2-2x+\frac{-2}{2}\\=2x^2-2x-1[/tex]
The answer is not one of the options which i assume might be a typing mistake.
Hence,
y+yz is: [tex]2x^2-2x-1[/tex]
