Basic Operations of Algebraic Symbols and Terms - JSS1 Mathematics Lesson Note

Addition and Subtraction:

When adding or subtracting algebraic expressions, you combine like terms. Like terms have the same variable part raised to the same power. For example, 

3𝑥 and 5𝑥 are like terms, but 

3𝑥 and 5𝑥2 are not.

Examples:

3𝑥+5𝑥:

Both terms have 𝑥, so add the coefficients.

3𝑥+5𝑥=8𝑥.

For 7𝑎2−3𝑎2:

Both terms have 

𝑎2, so subtract the coefficients.

7𝑎2−3𝑎2=4𝑎2.

2𝑥+3𝑦−𝑥+5𝑦:

Combine like terms (𝑥 terms together and 𝑦 terms together).

2𝑥−𝑥=𝑥 and 3𝑦+5𝑦=8𝑦.

The result is 𝑥+8𝑦.

Multiplication:

When multiplying algebraic expressions, you multiply the coefficients and add the exponents of like bases.

Examples:

3𝑥 x 2𝑥:

Multiply the coefficients (3 and 2).

Add the exponents of 

𝑥 (1 and 1).

3x2=6 and 𝑥1⋅

The result is 

6𝑥2.

(2𝑎)(−3𝑏):

Multiply the coefficients (2 and -3).

Since 𝑎 and 𝑏 are different variables, just multiply the variables.

2x−3=−6. The result is −6𝑎𝑏.

Division:

When dividing algebraic expressions, you divide the coefficients and subtract the exponents of like bases.

Examples:

6𝑥/3𝑥:

Divide the coefficients (6 and 3).

Subtract the exponents of 𝑥 (3 and 1).

6/3=2 and 𝑥(3−1)=𝑥2.

The result is 

2𝑥.

8𝑎/2𝑎:

Divide the coefficients (8 and 2).

Subtract the exponents of 𝑎 (4 and 2).

8/2 = 4 and 𝑎4−2=𝑎2.

The result is 

4𝑎2.