SaiBook.us Algebra

Lesson Example Discussion Quiz: Class Homework

Example

Title: Adding and subtracting polynomials

Grade: 8-b Lesson: S1-L1

Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Add the polynomials \$ - 7s^2 - 10s + 13\$ and \$ 15s^2+ 2(8s) + 5\$, then subtract the polynomial \$ 5s^2 -9s +7\$.

Step 1a

The given polynomials are \$ - 7s^2 - 10s + 13\$ and \$ 15s^2+ 2(8s) + 5\$, \$ 5s^2 -9s +7\$.

Simplify the expression: \$ - 7s^2 - 10s + 13\$ + \$15s^2 + 16s +5\$.

Combine the like terms: \$ (- 7s^2 + 15s^2) + (- 10s + 16s) + (13 + 5) \$.

Simplify the polynomials expression: \$ 8s^2 + 6s + 18\$.

Explanation: Here, simplify the given expression, then add the first two polynomial expressions together.

Step 1b

Subtract the polynomial \$ 5s^2 -9s +7\$ from the result obtained in the above step.

Rewrite the subtraction as adding the opposite: \$( 8s^2 + 6s + 18) - ( 5s^2 - 9s + 7)\$.

Distribute the negative sign to the polynomial expression: \$ 8s^2 + 6s + 18 - 5s^2 + 9s - 7\$.

Simplify the expression: \$ 3s^2 + 15s + 11\$.

Explanation: Subtract the polynomial expression from the previous result and simplify to obtain \$3s^2 + 15s + 11\$ as the final simplified expression.