Topics › KS3 › Algebra

Expanding brackets

exp-01 Present from here

Expand $3(x + 4)$

Option A: $3x + 4$

Option B: $3x + 7$

Option C: $12x$

Option D: $3x + 12$

Answer and misconceptions

Option A: $3x + 4$ ✗
Multiplies only the first term in the bracketMultiplies x by 3 but leaves the 4 unchanged.

Option B: $3x + 7$ ✗
Adds the outside number to the second termMultiplies 3 by x but adds 3 to 4 instead of multiplying.

Option C: $12x$ ✗
Combines unlike terms inside the bracketTurns x + 4 into 4x, then multiplies by 3.

Option D: $3x + 12$ ✓ Correct
exp-02 Present from here

Expand $-2(x - 5)$

Option A: $-2x + 10$

Option B: $-2x - 10$

Option C: $-2x - 5$

Option D: $2x - 10$

Answer and misconceptions

Option A: $-2x + 10$ ✓ Correct

Option B: $-2x - 10$ ✗
Thinks negative × negative is negativeWorks out −2 × −5 as −10.

Option C: $-2x - 5$ ✗
Multiplies only the first term in the bracketMultiplies x by −2 but copies the −5 unchanged.

Option D: $2x - 10$ ✗
Ignores the negative sign outside the bracketMultiplies by 2 instead of −2.
exp-03 Present from here

Expand $x(x + 3)$

Option A: $x^2 + 3$

Option B: $5x$

Option C: $x^2 + 3x$

Option D: $3x^2$

Answer and misconceptions

Option A: $x^2 + 3$ ✗
Multiplies only the first term in the bracketMultiplies x by x but leaves the 3 unchanged.

Option B: $5x$ ✗
Thinks x × x = 2xWorks out x × x as 2x, then adds the 3x to get 5x.

Option C: $x^2 + 3x$ ✓ Correct

Option D: $3x^2$ ✗
Multiplies all the terms togetherTreats x(x + 3) as x × x × 3.
exp-04 Present from here

Expand $(x + 2)(x + 5)$

Option A: $x^2 + 10$

Option B: $x^2 + 7x + 10$

Option C: $x^2 + 7x + 7$

Option D: $x^2 + 10x + 10$

Answer and misconceptions

Option A: $x^2 + 10$ ✗
Multiplies only firsts and lastsMultiplies x by x and 2 by 5 but misses the two x terms.

Option B: $x^2 + 7x + 10$ ✓ Correct

Option C: $x^2 + 7x + 7$ ✗
Adds the constants instead of multiplyingGets the x terms right but works out 2 + 5 for the last term.

Option D: $x^2 + 10x + 10$ ✗
Multiplies the numbers to get the x termThinks the coefficient of x is 2 × 5 instead of 2 + 5.
exp-05 Present from here

Expand $(x - 3)^2$

Option A: $2x - 6$

Option B: $x^2 + 9$

Option C: $x^2 - 6x + 9$

Option D: $x^2 - 6x - 9$

Answer and misconceptions

Option A: $2x - 6$ ✗
Thinks squaring means multiplying by 2Treats (x − 3)² as 2(x − 3).

Option B: $x^2 + 9$ ✗
Squares each term separatelyThinks (x − 3)² = x² + (−3)², missing the middle terms.

Option C: $x^2 - 6x + 9$ ✓ Correct

Option D: $x^2 - 6x - 9$ ✗
Thinks (−3) × (−3) = −9Expands correctly but gets the sign of the constant wrong.