Algebra is one of the most important topics that secondary students must master to do well in their mathematics assessments. Lower Secondary students usually struggle at the beginning when it comes to algebraic manipulation and solving of algebraic sums. 
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Here are some essential algebra rules that would help students a lot in scoring well in this subject and topic:
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1. Only combine LIKE terms
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Students MUST know:

• only like terms combine.

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Examples:

• 3x+2x=5x

• 4a−a=3a

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BUT:

• 3x+2y  cannot simplify further.

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This is one of the earliest algebra mistakes.

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2.  Distributive Law

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One of the MOST important rules.

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a(b+c)=ab+ac

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Examples:

• 3(x+2)=3x+6

• −2(a−5)=−2a+10

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Common mistake:

forgetting negative signs.

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3. Signs Matter

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Students lose MANY marks due to negatives.

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Examples:

• (−)(−)=(+)

• (−)(+)=(−)

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Especially important in:

• expansion

• factorisation

• solving equations

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4. Laws of Indices

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Essential for upper secondary.

Key rules:

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​Students often:

• add powers incorrectly,

• or mix multiplication/division rules.

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5. Fractions Must Follow Fraction Rules

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Students cannot:

• cancel terms across addition.

Wrong:

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unless separated properly.

Also:

• denominators must be the same before adding/subtracting.

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6. What You Do to One Side, Do to the Other

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Core equation-solving principle.

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Example:

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                2x+3=11

 

 

Subtract 3 from BOTH sides.

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This develops equation balance understanding.

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7. Expanding ≠ Factorising

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Students confuse these constantly.​​​​​​​