Presentation on theme: "Revision - Algebra I Binomial Product"— Presentation transcript:
1Revision - Algebra I Binomial Product Using Distributive Law toExpand / Remove Brackets.By I Porter
2Definitions Binomial Products Grouping symbols (…..) can be expanded by using the Disributlive Law.This states that for any real numbers a, b and c:a(b ± c) = ab ± acExamples:5(2+3) = 5 x x 3 3(7 - 4) = 3 x x 45 x 5 = x 3 =25 = 25 9 = 9Binomial ProductsA binomial expression contains two (2) terms such as : (2 + n), (2x - 5), (3n - 5p)A binomial product is the multiplication of two such binomial expression:(2 + n)(2x - 5), (a - b) (a + b), (2n - 5)(3n + 2), (3p + 4)2.The product of two binomials can be obtained using two approaches:a) the Geometrical Approach - using area diagrams.b) the Algebraic Approach - using the distributive law.
3Example: Expand (a + 4) ( a + 2) Algebraic Method By the distributive law:Geometrical MethodL = last termsI = inside terms(a + 4)(a + 2), can be represented by the area of a rectangle withsides (a + 4) and (a + 2).Area of the rectangle = length x breadth(a + 4)(a + 2) =aa+ 2)(+ 4a+ 2()O = outside termsF = first terms= a2 + 2a + 4a + 8a+ 2+ 4()Area == a2 + 6a + 8The area of the large rectangle is equal to the sum of the areas of all the smaller rectangles.F+O+I+L. method of distributive law.a+ 4+ 2FOIL is a mnemonic - a memory jogger - indicating orderof multiplication (don’t forget negative signs).F = a x a = a 2a2+ 4a+ 2a+ 8O = a x +2 = +2 aI = +4 x a = +4 aL = +4 x +2 = +8So, (a + 4)(a + 2)= a2 + 4a + 2a + 8= a2 + 6a + 8(a+4)(a+2)= a2 + 4a + 2a + 8= a2 + 6a + 8The algebraic method(s) are the preferred.