Examples · Algebra
Simplify Examples: 8 Worked Problems
Eight expressions, ordered so each one adds exactly one new idea to the last — every answer here is checked against the original by substituting a value for x.
Distributing a single term
- 4(x + 2) − 3xthe expression
- 4x + 8 − 3xdistribute the 4 across both terms inside
- x + 8combine the two x terms
Only one pair of like terms exists here, so combining is a single subtraction once distribution is done.
Distributing a negative coefficient
- −3(2x − 4)the expression
- −6x + 12the negative flips the sign of both terms inside
Distributing across two sets of parentheses
- 2(x − 1) + 5(x + 3)the expression
- 2x − 2 + 5x + 15distribute each term separately
- 7x + 13combine the x terms, then the constant terms
Each set of parentheses distributes on its own — the two brackets do not interact until the combining step gathers every like term from both at once.
Subtracting an entire parenthesised expression
- 5 − (2x + 3)the expression
- 5 − 2x − 3distribute the implied −1 across both terms
- −2x + 2combine the constant terms
Multiplying two parentheses together
- (x + 1)(x + 6)the expression
- x² + 6x + x + 6distribute every term in the first bracket across every term in the second
- x² + 7x + 6combine the two x terms
- (2x − 1)(x + 4)the expression
- 2x² + 8x − x − 4distribute every term across every term
- 2x² + 7x − 4combine the two x terms
Both examples need four multiplications for two two-term brackets — every term in the first has to reach every term in the second, not just line up with the term directly across from it.
A variable multiplying parentheses
- x(x + 2) − 3xthe expression
- x² + 2x − 3xdistribute x across both terms inside
- x² − xcombine the two x terms
Distributing x works the same way as distributing a number — every term inside the parentheses gets multiplied by it, here raising each x term's degree by one.
Terms of different degrees, already expanded
- 3x² + 2x − x² + 5xthe expression — no parentheses to distribute
- 2x² + 7xcombine the x² terms, then the x terms, separately
With nothing to distribute, simplifying is just the combining step — but it still only combines terms that share the exact same degree, x² with x² and x with x, never across the two.
Checking every result the same way
Substitute a number for x into both the original and the simplified expression.
| Example | At x = 2 | Original | Simplified |
|---|---|---|---|
| 1 | 4(2+2) − 3(2) = 16 − 6 | 10 | 2 + 8 = 10 ✓ |
| 3 | 2(1) + 5(5) = 2 + 25 | 27 | 7(2) + 13 = 27 ✓ |
| 5 | (3)(8) | 24 | 4 + 14 + 6 = 24 ✓ |
This is exactly the check the Simplify Calculator on this site runs internally, at several values of x, before showing any result — not just trusting the distribution and combining steps blindly. To check the answer yourself, pick any number for x and confirm both forms give the same result.
What all eight worked examples have in common
Every one of these worked examples is the same two moves in the same order: apply the distributive property to remove parentheses, then combine like terms by adding coefficients of matching powers. A product of two brackets and a single-term distribution are not different techniques — a polynomial like x² + 7x + 6 is simply what the same rule produces when applied to a larger starting expression.
The negative sign deserves the most care in every example above. It travels with the term it belongs to through distribution and again through combining, and the degree of a term — the power of x it carries — decides which terms are allowed to meet at the combining step at all.
Questions about simplify examples
What is 4(x + 2) − 3x simplified?
x + 8. Distribute the 4 to get 4x + 8 − 3x, then combine the two x terms.
What is −3(2x − 4) simplified?
−6x + 12. The negative distributes across both terms, and a negative times a negative gives the positive 12.
How do I simplify (x + 1)(x + 6)?
Distribute every term in the first bracket across every term in the second: x² + 6x + x + 6, which combines to x² + 7x + 6.
How do I check a simplified expression is correct?
Substitute the same number for x into both the original and the simplified expression. They must produce the exact same result.