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