Expanding and Collecting Like Terms (VCE SSCE Mathematical Methods): Flashcards

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Expanding and collecting like terms
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Like terms

Terms with the same variable parts

Expanding single bracket rule

Multiply term outside by each term inside

Negative sign outside bracket effect

Changes sign of every term inside when expanded

Multiplying same base variables rule

Add the powers

(a+b)(c+d)(a+b)(c+d) expanded

ac+ad+bc+bdac + ad + bc + bd

(a+b)2(a+b)^2 expanded

a2+2ab+b2a^2 + 2ab + b^2

Perfect square pattern memory aid

Square first, square last, twice the product in between

(a+b)(ab)(a+b)(a-b) expanded

a2b2a^2 - b^2

Difference of two squares - what cancels?

The middle terms cancel out

General principle for any bracket expansion

Each term in first bracket multiplies each term in second

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