Perform the following additions and/or subtractions:

$\left(9 b^2+6 b+5\right)+\left(3 b^2+5 b+4\right)=$

Combine the b 2 terms: 9 b 2 + 3 b 2 = 12 b 2 .
Combine the b terms: 6 b + 5 b = 11 b .
Combine the constant terms: 5 + 4 = 9 .
The resulting polynomial is: 12 b 2 + 11 b + 9 ​ .

Explanation

Understanding the Problem We are asked to add two polynomials: ( 9 b 2 + 6 b + 5 ) and ( 3 b 2 + 5 b + 4 ) . To do this, we combine like terms.

Grouping Like Terms First, let's group the like terms together:


( 9 b 2 + 3 b 2 ) + ( 6 b + 5 b ) + ( 5 + 4 )

Adding b 2 Terms Now, we add the coefficients of the b 2 terms:

9 b 2 + 3 b 2 = ( 9 + 3 ) b 2 = 12 b 2

Adding b Terms Next, we add the coefficients of the b terms:

6 b + 5 b = ( 6 + 5 ) b = 11 b

Adding Constant Terms Finally, we add the constant terms:

5 + 4 = 9

Final Result Combining these results, we get the final polynomial:

12 b 2 + 11 b + 9
Examples
Polynomial addition is used in various fields such as engineering, physics, and computer graphics. For example, in computer graphics, polynomials can represent curves and surfaces. Adding polynomials allows us to combine these curves or surfaces to create more complex shapes. In physics, polynomials can describe the motion of objects, and adding them can help analyze the combined motion of multiple objects.

Answered by GinnyAnswer | 2025-07-07