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About this video
Multiplying out brackets with the distributive property — the term outside times every term inside, adding the exponents of the same letter — and then collecting like terms.
What it covers
- The distributive property: multiply every term inside the bracket
- The same letter: add the exponents (x × x = x², not 2x)
- The sign belongs to the term (it is −4, not 4)
- Two brackets, then like terms: the same letter AND the same exponent
- A coefficient of 0 makes the term fall away
Extra worked examples
✍️ Extra example: expand −3x²(2x³ − x + 4)
- 1−3x² × 2x³ = −6x⁵Numbers first (−3 × 2 = −6), then the letters: add the exponents, 2 + 3 = 5.
- 2−3x² × (−x) = +3x³Negative × negative is positive; x has an exponent of 1, so 2 + 1 = 3.
- 3−3x² × 4 = −12x²A number: the letter simply comes along.
- 4= −6x⁵ + 3x³ − 12x²No like terms — stop there.
✍️ Extra example: simplify 4(2x − 3) − 2(x² + 3x − 5)
- 18x − 12 − 2x² − 6x + 10Multiply the 4 into its bracket, and the −2 — sign included — into the other.
- 2−2x² + (8x − 6x) + (−12 + 10)Like terms: the same letter and the same exponent; the numbers are like terms too.
- 3= −2x² + 2x − 2Nothing else is alike, so this is the answer.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Expand 5(x + 6).
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5x + 30 - 2Expand x(x² − 4x + 7).
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x³ − 4x² + 7x - 3Expand −2a²(3a − 5).
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−6a³ + 10a² - 4Simplify 3(2x + 4) + 5x.
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6x + 12 + 5x = 11x + 12 (the 5x is not inside the bracket) - 5Simplify −2(x² − 3x + 1) + 2(x² + x).
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−2x² + 6x − 2 + 2x² + 2x = 8x − 2 (0x² falls away)
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