To solve the problem of subtracting the polynomial 2y² + 3y + 5 from y³ + 6y² + 5y, we need to perform the following calculation:
(y³ + 6y² + 5y) – (2y² + 3y + 5)
Let’s break this down step-by-step:
- Align the polynomials:
We will first write both polynomials in standard form, aligning like terms:
y³ + 6y² + 5y
– 2y² + 3y + 5 - Subtract like terms:
We subtract the coefficients of like terms:- For y³: y³ remains y³
- For y²: 6y² – 2y² = 4y²
- For y: 5y – 3y = 2y
- For the constant term: 0 – 5 = -5
Putting it all together:
After doing the subtraction, we get:
Result: y³ + 4y² + 2y – 5
This means that the final simplified expression after the subtraction is:
y³ + 4y² + 2y – 5
And that’s the answer!