This pdf includes the following topics:- Expanding brackets FOIL Distributive Law Distributive properties Examples
1. Student Learning Expanding Brackets Centre Expanding brackets Expanding is to remove brackets from an algebraic expression. FOIL is called the Distributive Law: (a+b)(c+d) = ac+ad+bc+bd FOIL Expand For example : factoring 2y + 6 2 𝑦𝑦 + 3 2𝑦𝑦 + 6 both 2y and 6 have a common factor of 2 2y is 2 × y 6 is 2 × 3 So you can factor the whole expression into: 2y+6 = 2(y+3) Factor Find the product (m – 1)(-4m – 4) To simplify the product of two binomials, use the distributive property. Use the FOIL method. Find the products of the First, Outside, Inside, and Last terms, and then add them. Use the distributive property to simplify (m – 1)(-4m – 4). You can use the FOIL method: Multiply the first terms of (m – 1)(-4m – 4): (m)(-4m) = -4m2 Multiply the outside terms of (m – 1)(-4m – 4): (m)(-4) = -4m Multiply the inside terms of (m – 1)(-4m – 4): (-1)(-4m) = 4m Multiply the last terms of (m – 1)(-4m – 4) : (-1)(-4) = 4 Finally, add these results and simplify. -4m2 + -4m + 4m + 4 -4m2 + 4 Expanding Brackets 5/2013 @ SLC 1 of 2
2. DISTRIBUTIVE PROPERTIES The Distributive Properties rules tell us that if you have a term being multiplied by two or more terms being either added or subtracted within brackets (parenthesis), the term outside the brackets must be multiplied by EVERY term within the brackets. STUDENT LEARNING CENTRE REGISTRY BUILDING ANNEXE TEL: 61-8-8201 2518 E-MAIL: slc@flinders.edu.au INTERNET: http://www.flinders.edu.au/SLC POSTAL: PO BOX 2100, ADELAIDE, SA 5001 Expanding Brackets 5/2013 @ SLC 2 of 2
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