Algebraic Manipulation

Algebraic Manipulation

1. Expanding Brackets

   • To expand or multiply out this expression we multiply every term inside the bracket by the them outside the bracket
   • 3y(4-2y)= 12y-6y^2
   • when there is a negative term outside the bracket , the signs of the multiple terms change

2. Simplifying brackets

   • sometimes you need to expand the bracket and the simplify the bracket
     • 3x+2x(5-x)=3x+10x-2x^2=13x-2x^2

3. Expanding Two Brackets

   • to multiply two brackets we multiply every term in the second bracket to every term in the first bracket
   • (x+y)(x+y) = x^2+xy+y^2
   • with practice you can expand two brackets in a simpler form

4. Squaring Expressions

   • (2-3a)^2=4-12a+9a^2
   • the first term is squared
   • the second one is the product of the two terms
   • the third one is squared

5. differences between two squares

   • when we simplify the two the middle number cancel out
   • (a-b)(a+b)=A^2-b^2

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