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D-6MathsFri 4 Sept

Algebra: expand & simplify

Signs and like terms — the quiet mark-losers.

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Expanding is just multiplying every term inside the bracket. The mark is lost when the minus outside the second bracket is ignored — it has to hit both terms, not only the first.

Picture it: the minus must reach both terms

3(2x + 5) − 2(x − 4)

−2 × (x − 4)−2x+8

Rushed: 6x + 15 − 2x − 4

Minus only hit the first term

Careful: 6x + 15 − 2x + 8

−2 × (−4) becomes +8

Remember — distribute, then collect

  1. Multiply the outside number by every term in the bracket.
  2. A minus in front flips every sign inside.
  3. Collect like terms last: x-terms together, numbers together.

Exam trap

Options include the version where only the first term was multiplied, and the version where −(x − 4) became −x − 4. Expand on paper before you look at the choices.

Question patterns you might see

Same expand. Watch the hidden plus.

  1. 1 · Simple — Single bracket

    “Expand 4(3x + 2)”

    4 × 3x

    12x

    →

    4 × 2

    8

    →

    Result

    12x + 8

  2. 2 · Simple — Minus outside

    Expand 5(x + 3) − 2(x + 1)

    1. 15x + 15
    2. 2− 2x − 2
    3. 3Collect: 3x + 13

    3x + 13

  3. 3 · Medium — Minus times a minus

    Expand 3(2x + 5) − 2(x − 4)

    1. 13 × 2x = 6x, 3 × 5 = 15 → 6x + 15
    2. 2−2 × x = −2x, −2 × (−4) = +8 → −2x + 8
    3. 36x − 2x + 15 + 8 = 4x + 23

    4x + 23

  4. 4 · Trickier — Then solve

    “Solve 2(x + 4) = 3(x − 1)”

    1. 12x + 8 = 3x − 3
    2. 28 + 3 = 3x − 2x
    3. 311 = x

    x = 11

Coach tip: rewrite a minus in front as “multiply by −1” before you touch the options.

Tomorrow (D-5): mean and median — the average they ask for is not always the mean.

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