Practice Questions
Concept Explanation
Simplification means reducing an algebraic expression to its simplest form by combining like terms and applying order of operations (BODMAS).
Rules
- Combine like terms: 3x + 5x = 8x
- Distribute: a(b + c) = ab + ac
- Remove brackets carefully, respecting signs
Example
Simplify 2(3x + 4) − 3(x − 2) = 6x + 8 − 3x + 6 = 3x + 14.
Common Trap
Minus before a bracket changes every sign inside: −(x − 3) = −x + 3.
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Q1 EasyWhat is the simplified form of the expression 3x + 5x − 2x?Explanation3 + 5 − 2 = 6, so 6x.
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Q2 EasyWhat is the fully simplified value of 2(x + 3) + 4?Explanation2x + 6 + 4 = 2x + 10.
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Q3 EasyWhat does the expression 5a − 2(a + 3) simplify to?Explanation5a − 2a − 6 = 3a − 6.
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Q4 EasyWhen (x + 2) and (3x − 5) are added and like terms are combined, what is the result?Explanation4x − 3.
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Q5 EasyFor x ≠ 0, what is 3/x + 2/x equal to when written as a single fraction?ExplanationLike denominators: (3 + 2)/x = 5/x.
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Q6 MediumWhat is the simplified form of 4(2x − 1) − 2(x + 3)?Explanation8x − 4 − 2x − 6 = 6x − 10.
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Q7 MediumWhat is the simplified form of 3x² + 2x − x² + 5x?Explanation2x² + 7x.
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Q8 MediumWhat does −(x − 4) + 2x simplify to when the brackets are removed and like terms are combined?Explanation−x + 4 + 2x = x + 4.
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Q9 MediumWhat is the simplified value of 2[3x − (x + 1)]?Explanation2[2x − 1] = 4x − 2.
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Q10 MediumIf 2x + 3y = 12, what is the value of 4x + 6y?Explanation4x + 6y = 2(2x + 3y) = 2 × 12 = 24.
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Q11 MediumWhat is the simplified form of x(x + 1) + x(x − 1)?Explanationx² + x + x² − x = 2x².
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Q12 HardAfter expanding and simplifying (x + 1)(x + 2) − x(x + 3), what do you obtain?Explanationx² + 3x + 2 − x² − 3x = 2.
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Q13 HardWhat is the fully simplified form of 5(x − 2) − 3(2x − 1) + x?Explanation5x − 10 − 6x + 3 + x = 0.
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Q14 HardWhat is the simplified form of (a + b)² − (a − b)²?ExplanationExpanded difference gives 4ab.
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DS1 Easy
What is the simplified value of the expression 2x + 3x?
Statement Ix = 4.
Statement IIThe expression has two like terms in x.
ExplanationStatement I alone: 5x = 20. Statement II describes form only. -
DS2 Easy
What is the simplified value of 2[x − (x − 3)]?
Statement IThe inner bracket simplifies to 3.
Statement IIx is any real number.
ExplanationStatement I alone: 2 × 3 = 6 for all x.
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DS3 Medium
What is the simplified form of 3(a + b) − 2a?
Statement Ia = 5.
Statement IIb = 2.
ExplanationNeed both: 3(7) − 10 = 11, or a + 3b = 11. -
DS4 Medium
What is the simplified form of 4x − 2(x + 1)?
Statement Ix = 6.
Statement IIThe simplified form is 2x − 2.
ExplanationStatement I alone: 2(6) − 2 = 10.