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Learning Algebra 1 includes the subsequent topics like addition and subtraction of algebraic expression, multiplication, and division of polynomials, resolution polynomials, graphing linear and quadratic relations and functions, exponents and irrational numbers, how to solve equations, change expressions and resolution of worldly issues. Students learn to study patterns and relationships, formalizing their data, learning to use symbolic notation. When students create the transition from concrete arithmetic to the symbolic language of algebra one, they develop abstract reasoning skills necessary to surpass in mathematics and science.

**Example 1: **

Subtract 7p – 2q – 5r from the sum of 5p + 2q - 3r + 1 and 3p – 4r – 3

**Solution:**

5p + 2q - 3r + 1

3p – 4r – 3

7p – 2q – 5r [we need to change the sign of each term of the third expression as it is to be subtracted and then add]

Subtract 7p – 2q – 5r from the sum of 5p + 2q - 3r + 1 and 3p – 4r – 3

5p + 2q - 3r + 1

3p – 4r – 3

7p – 2q – 5r [we need to change the sign of each term of the third expression as it is to be subtracted and then add]

p + 4q – 2r – 2

**Example 2: **

The sum of the digits of a two digit number is 12. If 18 are added to it, the digits are reversed so the number will be ___ .

**Solution:**

Let the unit digit be x

The sum of both the digit is 12, the tens digit = 12 – x

So the number = (12 – x ) * 10 + x

On reversing the digits, x is at tens; (12 – x) at unit.

New number = x *10 + (12 – x)

x *10 + (12 – x) = (12 – x ) * 10 + x + 18

9x + 12 = - 9x + 138

18x = 126

x = 7

The number is 57.

The sum of the digits of a two digit number is 12. If 18 are added to it, the digits are reversed so the number will be ___ .

Let the unit digit be x

The sum of both the digit is 12, the tens digit = 12 – x

So the number = (12 – x ) * 10 + x

On reversing the digits, x is at tens; (12 – x) at unit.

New number = x *10 + (12 – x)

x *10 + (12 – x) = (12 – x ) * 10 + x + 18

9x + 12 = - 9x + 138

18x = 126

x = 7

The number is 57.