How to simplify Variable Expressions

How to simplify Variable Expressions

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Expressions are defined as an algebraic statement which contains several terms which are separated by mathematical operations. Now, these terms could be pure variable terms, pure constant terms, or even mixed terms such as variables with coefficients. 

Simplifying Variable Expressions

To simplify variable expressions, we must use 2 techniques:

  • Firstly, we must add or subtract like terms like those with the same variable (like 3x, 7x) or those with the same powers (like 2x2, 3x2)
  • Next, we must apply distributive law if possible. The distributive property states that multiplication distributes over addition, i.e., x(y + z) = (xy + xz).

Example 1: 2x2(7x + 9) + x2 = 2x2(7x) + 2x2(9) + x2= 14x3 + 18x2 + x2 = 14x3 + 19x2

Example 2: 7x2(3x + 5) + x2 = 7x2(3x) + 7x2(5) + x2 = 21x3 + 35x2 +x2 = 21x3 + 36x2

Example 3: x3(x + 4) + 8x2 = x3(x) + x3(4) + 8x2 = x4 + 4x3 + 8x2

Example 4: x2(x  7) + 2x2 = x2(x) + x2(7) + 2x2 = x3  7x2 + 2x2 = x3  5x2

Example 5: x2(x  3) + x2(x + 8) = x2(x) + x2(3) + x2(x) + x2(8) = x3  3x2 + x3 + 8x2 = 2x3 + 5x2

Example 6: 2x2(x + 6)  x2(x + 7) = 2x2(x) + 2x2(6)  x2(x)  x2(7) = 2x3 + 12x2  x3  7x2 = x3 + 5x2

Example 7: x3(x  4) + x3(x  8) = x3(x) + x3(4) + x3(x)+ x3(8) = x4  4x3 + x4  8x3 = 2x4  12x3

Free printable Worksheets

Exercises for Simplifying Variable Expressions

1) 19x2 (7x + x) + x3 =

2) 18x2 (7x + x) + x3 =

3) 17x2 (6x + x) + x3 =

4) 16x2 (2x + x) + x3 =

5) 15x2 (4x + x) + x3 =

6) 18x2 (5x) =

7) 20x2 (5x + x) =

8) 12x2 (2x + x) =

9) 5x2 (7x + x) =

10) 3x2 (3x) =

 
1) 19x2 (7x + x) + x3 =153x3
2) 18x2 (7x + x) + x3 =145x3
3) 17x2 (6x + x) + x3 =120x3
4) 16x2 (2x + x) + x3 =49x3
5) 15x2 (4x + x) + x3 =76x3
6) 18x2 (5x) =90x3
7) 20x2 (5x + x) =120x3
8) 12x2 (2x + x) =36x3
9) 5x2 (7x + x) =40x3
10) 3x2 (3x) =9x3

Simplifying Variable Expressions Practice Quiz