Summary of "Expanding and factorising brackets"
Overview
The video gives three worked examples demonstrating how to expand and how to factorise algebraic brackets. General lessons:
- To expand: multiply out each bracket and combine like terms.
- To factorise: extract the common numerical and variable factors.
Examples and step-by-step methods
1) Expanding a sum of two linear brackets (expand then simplify)
Method:
- Expand each bracket (multiply coefficients by the variable and constants).
- Combine like terms (collect x-terms and constant terms).
Worked result:
- After expanding both brackets and combining like terms the final simplified result is 13x + 10.
2) Expanding (multiplying) two linear brackets — FOIL / “smiley face” method
Method (FOIL / “smiley face”):
- First: multiply the x-terms (gives x^2 terms).
- Outer: multiply the outer terms.
- Inner: multiply the inner terms.
- Last: multiply the constant terms.
- Then collect and simplify like terms.
Worked steps (as presented):
- 2x * x → 2x^2
- 1 * x → + x
- 2x * (−4) → −8x
- 1 * (−4) → −4
- Combine the x-terms: x + (−8x) = −7x
Final simplified answer:
- 2x^2 − 7x − 4
3) Factorising by taking out a common factor
Method:
- Look for the greatest common numerical factor of all terms.
- Look for the common variable factor (lowest power of any shared variable).
- Factor that common term out, writing what remains in the bracket.
- Check by multiplying back to ensure you recover the original expression.
Worked idea shown:
- The terms share a common factor 3 and a common factor y.
- Factor out 3y.
Example factorisation:
- 6y^2 − 9xy = 3y(2y − 3x)
Quick check:
- 3y × 2y = 6y^2
- 3y × (−3x) = −9xy
- The factorisation is correct.
Speakers / sources
- Single unnamed instructor / narrator (video presenter).
Category
Educational
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