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Algebraic Expressions & Substitution
Rung 3 of 4 · The traps

2x Is Not X²

Three little slips swallow more marks than anything else in early algebra. Let's make each one impossible to fall for.


ExploreSlide x and compare. Then hit “try a negative x” and watch the sign.
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Substitution itself is easy. What trips people up is reading the expression correctly before they drop the number in. Three traps do most of the damage.

Trap One: X² Is Not 2x

This is the big one. 2x means 2 times x. means x times x — the little 2 says "use it as a factor twice", it does not mean "times two". With x = 5: 2x = 10 but x² = 25. Totally different numbers. The toy shows them side by side — slide x and watch the gap open up. They only ever match at x = 0 and x = 2.

Say it plainly: 2x = x + x (twice the value). x² = x × x (the value times itself). Read the position of the 2: in front means multiply, up top means power.

Trap Two: Negatives Need Brackets

When the value is negative, wrap it in brackets as you substitute — it saves you every time. Evaluate at x = −4: write (−4)², which is −4 × −4 = 16, a positive answer, because a negative times a negative is positive. Skip the brackets and you'll wrongly write −4² and get −16. The brackets keep the minus sign attached to the number.

Trap Three: Order of Operations Still Rules

After you substitute, the sum is ordinary arithmetic — so the ordinary order applies. In 3a − 4 you multiply before you subtract. In a² + 1 you square before you add. Don't just work left to right; let brackets, indices, then ×/÷, then +/− decide the order.

Us, Thinking Out Loud

Explain to me, in your own words, why x² and 2x aren't the same.

Why does squaring a negative give a positive?