Guide · For JSS 2 – SS 2 students · 7 min read

10 algebra mistakes students make (and how to fix each one)

The ten slips that cost students the most marks in algebra, from sign errors and wrong cancelling to forgetting to flip an inequality. For each one: what it looks like, why it is wrong and the correct working.

By the MathPlug team, Reflex System · Published 5 October 2026

Most marks lost in algebra are not lost because a student does not understand the topic. They are lost to small, repeated slips: a minus sign that disappears, a term that gets cancelled when it shouldn't, a bracket that is squared the wrong way.

The good news is that these slips are predictable. The same ten turn up again and again in class tests, BECE scripts and WASSCE scripts. Once you know what they look like, you can catch them before they cost you. For each mistake below you will see the wrong working, why it is wrong, and the correct working.

Brackets and signs

Mistake 1: losing the sign when there is a minus outside a bracket. Simplify 5 − (x − 3).

Wrong: 5 − x − 3 = 2 − x
Why it's wrong: the minus sign belongs to everything inside the bracket. It changes −3 into +3, not only x into −x.
Right: 5 − x + 3 = 8 − x
Check with x = 1: 5 − (1 − 3) = 5 − (−2) = 7, and 8 − 1 = 7. The wrong answer gives 2 − 1 = 1.

Mistake 2: multiplying only the first term. Expand 3(2x + 4).

Wrong: 3(2x + 4) = 6x + 4
Why it's wrong: the 3 multiplies every term inside the bracket, not just the first one.
Right: 3(2x + 4) = 3 × 2x + 3 × 4 = 6x + 12

💡 Tip: Draw a small arrow from the number outside the bracket to each term inside before you multiply. One arrow per term means no term is forgotten. Our lesson on expanding brackets has more practice.

Like terms and squared brackets

Mistake 3: adding terms that are not alike. Simplify 3x + 2y and 4a + 3b − a + 2b.

Wrong: 3x + 2y = 5xy
Why it's wrong: x and y stand for different numbers. Three oranges and two mangoes are not five "orange-mangoes". You can only add like terms: the same letters with the same powers.
Right: 3x + 2y cannot be simplified. It is already in its simplest form.
And: 4a + 3b − a + 2b = (4a − a) + (3b + 2b) = 3a + 5b

Mistake 4: squaring each term of a bracket. Expand (x + 3)².

Wrong: (x + 3)² = x² + 9
Why it's wrong: (x + 3)² means (x + 3)(x + 3). Every term in the first bracket multiplies every term in the second, which gives two middle terms you must not lose.
Right: (x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9
Check with x = 1: (1 + 3)² = 16, and 1 + 6 + 9 = 16. The wrong answer gives 1 + 9 = 10.

In general, (a + b)² = a² + 2ab + b², never a² + b². See the formula card for expanding perfect squares.

Fractions and division

Mistake 5: cancelling terms instead of factors. Simplify x + 4x + 2.

Wrong: cross out the x on top and bottom to get 42 = 2.
Why it's wrong: you may only cancel something that multiplies the whole top and the whole bottom. Here x is added, not multiplied. Try x = 2: 2 + 42 + 2 = 64 = 1.5, not 2.
Right: x + 4x + 2 does not simplify.
Compare: 3x + 6x + 2 = 3(x + 2)x + 2 = 3. This time (x + 2) is a factor of the top, so it can cancel.

Mistake 6: dividing only one term. Solve 2x + 6 = 10.

Wrong: divide by 2 to get x + 6 = 5, so x = −1.
Why it's wrong: when you divide one side by 2, every term on that side must be divided by 2.
Right: x + 3 = 5, so x = 2. (Or subtract 6 first: 2x = 4, so x = 2.)
Check: 2 × 2 + 6 = 10. Correct.

💡 Tip: Before you cancel anything in a fraction, ask: "Is this multiplying everything above and everything below?" If not, factorise first or leave it alone.

Equations and inequalities

Mistake 7: doing the wrong opposite operation. Solve 3x + 5 = 20.

Wrong: 3x = 20 + 5 = 25, so x = 253.
Why it's wrong: the 5 is added on the left, so you remove it by subtracting 5 from both sides, not adding.
Right: 3x = 20 − 5 = 15, so x = 5.
Check: 3 × 5 + 5 = 20. Correct.

Mistake 8: forgetting to flip the inequality sign. Solve −3x > 12.

Wrong: divide by −3 to get x > −4.
Why it's wrong: multiplying or dividing both sides by a negative number reverses the order. 2 < 5, but −2 > −5.
Right: x < −4.
Check with x = −5: −3 × (−5) = 15, and 15 > 12 is true. With x = 0: 0 > 12 is false, so x > −4 cannot be right.

Formulas and substitution

Mistake 9: change of subject in the wrong order. Make t the subject of v = u + at.

Wrong: t = va − u
Why it's wrong: to free t, undo what was done to it in reverse order. t was multiplied by a, then u was added. So subtract u first, then divide by a.
Right: v − u = at, so t = v − ua.
Check with u = 2, a = 3, t = 4: v = 2 + 3 × 4 = 14, and 14 − 23 = 4. Correct.

Mistake 10: substituting a negative number without brackets. Find x² + 2x when x = −3.

Wrong: −3² + 2 × −3 = −9 − 6 = −15
Why it's wrong: −3² means −(3²) = −9. But x² with x = −3 is (−3) × (−3) = 9.
Right: (−3)² + 2(−3) = 9 − 6 = 3

💡 Tip: Whenever you substitute a negative number, put it in brackets first, every time. This one habit removes a whole family of errors. Our substitution lesson lets you practise it.

How to stop making the same mistake twice

Knowing the mistakes is half the work. The other half is building habits that catch them:

Check by substituting. Pick a simple number such as x = 1 or x = 2 and put it into both the question and your answer. If the values differ, there is a slip somewhere.
Write one step per line. Most sign errors happen when two steps are squeezed into one.
Keep a mistakes notebook. Write each slip you make with the correct working beside it, and read it before every test. See our tip on keeping a mistakes notebook.
Say the rule out loud. "Minus outside changes every sign." "Cancel factors, not terms." Short rules are easy to remember under exam pressure.

In WASSCE Paper 2, examiners award marks for correct steps, so clear working also protects you: even if a slip creeps in late, the earlier correct steps can still earn marks.

Questions students ask

What are the most common algebra mistakes?: Sign errors when removing brackets, adding unlike terms, writing (a + b)² as a² + b², cancelling terms instead of factors, and forgetting to reverse an inequality sign when multiplying or dividing by a negative number.
Why is (a + b)² not equal to a² + b²?: Because (a + b)² means (a + b)(a + b). Multiplying it out gives a² + ab + ab + b² = a² + 2ab + b². Try a = 1 and b = 2: (1 + 2)² = 9, but 1 + 4 = 5.
When do you flip the inequality sign?: Only when you multiply or divide both sides by a negative number. Adding or subtracting, even a negative number, never changes the direction of the sign.
How can I check my algebra answer?: Substitute a simple number into both the original expression and your answer. For an equation, put your solution back into the original equation and see whether both sides are equal.

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