Q. 48 - Intermediate Algebra

Question

In the following exercises, subtract the polynomials. 

$\text{ Subtract }\left(5y^2-y+12\right)\text{ from }\left(10y^2-8y-20\right)$

Step-by-Step Solution

Answer

On subtracting $\left(5y^2-y+12\right)\text{ from }\left(10y^2-8y-20\right)$ we get $5y^2-7y-32$

Step 1. Given information

$\begin{array}{l}\text{The given expressions are}\\ \left(5y^2-y+12\right)\text{ and }\left(10y^2-8y-20\right)\\ \text{We have to subtract }\left(5y^2-y+12\right)\text{ from }\left(10y^2-8y-20\right)\\ i.e\text{ To find : }\left(10y^2-8y-20\right)-\left(5y^2-y+12\right)\end{array}$

Step 2. Subtract the polynomials

$\begin{array}{l}\Rightarrow \left(10y^2-8y-20\right)-\left(5y^2-y+12\right)\\ =10y^2-8y-20-5y^2+y-12\left[\text{Rewrite without parentheses}\right]\\ =10y^2-5y^2-8y+y-20-12\left[\text{Combine the like terms}\right]\\ =5y^2-7y-32\left[\text{Simplify}\right]\end{array}$