Algebra

Single-bracket expansion

Multiply every term inside the bracket.

Predict, test and explain

Step 1 of 3

Predict

What is −2(x − 3) after expanding?

3(x+2)3(x + 2)
33
1x1x
+2+2
    Check with a value of x

    3(1×(2)+2)=123(1\times(2)+2)=12
    3×(2)+6=123\times(2)+6=12

    The outside multiplier applies to every term in the bracket, including its sign.

    InvestigateWhy does the outside multiplier reach both terms?

    Explore and compare

    Choose the investigation above. Predict what will change before you move a control.

    Try it in the simulation. Change one thing at a time.

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    Hints, self-check and connections
    Try a self-check

    Fixed values, separate from the diagram controls.

    Expand this single bracket.

    −2(3x−5)-2(3x-5)

    Hint

    Multiply each whole signed term by the negative number outside.

    Reveal answer

    The first product is negative; the two negative signs in the second product give a positive result.

    −2(3x−5)=−6x+10-2(3x-5)=-6x+10

    Build an explanation

    Hint 1

    The multiplier outside a bracket applies to every term inside it.

    Hint 2

    For k(ax + b), calculate k × ax and k × b separately, keeping each term's sign.

    Hint 3

    A negative multiplier reverses each non-zero term's sign. A zero multiplier makes the whole expression zero.

    Worked example

    This example uses fixed values, separate from the diagram controls.

    Expand −3(2x − 4). What would 0(2x − 4) equal?

    1. Multiply −3 by the full first term: (−3) × 2x = −6x.
    2. Multiply −3 by the full second term, −4: (−3) × (−4) = 12.
    3. Combine the two products: −6x + 12.
    4. With multiplier zero, both products are zero: 0 × 2x + 0 × (−4) = 0.

    Answer: −3(2x − 4) = −6x + 12; 0(2x − 4) = 0.

    Connect this idea

    Watch out: Do not multiply only the first term. The second term includes its sign, so multiplying −4 by −3 gives +12.