Algebra - Expansion of Brackets

Algebra - Expansion of Brackets

1. We don't usually write x (times) in an equation when multiplying, we instead just put the number in front of the bracket. (Example: 3y(4-2y), not 3y x (4-2y)

2. Distributive Law

   • a(b+c)
     • We expand it by multiplying the number outside the bracket with both numbers inside the bracket.
   • (a+b)(c+d)
     • we do this by multiplying by using SLIP.

3. Perfect Squares

   • (a+b)^2
   • We get our answer by expanding the brackets, and then simplifying it later,
     • In general:

4. Difference of 2 Squares

   • (a+b)(a-b)
     • Method: We will first have to expand the brackets, which will be a^2 +ab -ab -b^2. We will then need to simplify the terms and it will become a^2 - b^2.
   • When we simplify, the two middle terms cancel out.
     • Examp,e:

5. Simplifying

   • We simplify equations by finding the common factors, and then we simplify.
   • This is so that we can see the equations in a much easier way.
   • Example:

6. Expanding

   • Expanding expression with brackets
     • When there is a negative term outside the bracket, the sign of the multiplied terms change.
       • Example:
     • To expand, we have to multiply every term inside a bracket by the term outside the bracket.
       • Example:
     • Expanding brackets and simplifying
       • Sometimes, we need to multiply out brackets then simplify.
         • Multiplying out both brackets or terms and collecting like terms.
       • Examples:
   • We have to multiply the bracket in order to expand it.

7. We expand expressions by using SLIP

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