Expanding Double Brackets Flashcards

All 6 cards in this deck

What are the steps to expand and simplify the product of two binomials?

e.g. (x+5)(x−9)(x+5)(x-9)

  1. Multiply each term in the first bracket by each term in the second: x2−9x+5x−45x^2-9x+5x-45
  2. Collect the like terms: x2−4x−45x^2-4x-45

How many terms do you get when expanding two binomials, before simplifying?

Four terms.
e.g. (x+5)(x−9)=x2−9x+5x−45(x+5)(x-9)=x^2-9x+5x-45

In the expansion of (x+a)(x+b)(x+a)(x+b), what are the coefficient of xx and the constant term?

Coefficient of xx is a+ba+b; constant term is abab.
e.g. (x+2)(x+5)=x2+7x+10(x+2)(x+5)=x^2+7x+10

How do you expand a squared bracket?

e.g. (2x−5)2(2x-5)^2

Write it as two brackets and expand.
(2x−5)(2x−5)=4x2−20x+25(2x-5)(2x-5)=4x^2-20x+25

True or false? (x+3)2=x2+9(x+3)^2=x^2+9.

False. (x+3)2=x2+6x+9(x+3)^2=x^2+6x+9 — the middle terms must be included.

True or false? (x−2)(x+5)(x-2)(x+5) and (x+5)(x−2)(x+5)(x-2) give the same expansion.

True. Multiplication is commutative, so the order of the two brackets does not change the result.