Quadratic

1. Factoring

1.1. Common Factoring

1.1.1. Factoring Trinominals (3 Terms)

1.1.1.1. Complex trinomial (when coefficient a > 1)

1.1.1.1.1. ax^2+ bx+c

1.1.1.2. Simple trinominal (when coefficient a is = 1)

1.1.1.2.1. x^2+bx+c

1.1.1.3. Perfect square trinominals

1.1.1.3.1. a^2+2ab+b^2=(a+b)^2

1.1.1.3.2. a^2-2ab+b^2=(a-b)^ 2

1.1.2. Factoring Binominals (2 terms)

1.1.2.1. Differences of squares

1.1.2.1.1. a^2-b^2=(a+b)(a-b)

1.1.2.2. Common factor Binominals

1.1.2.2.1. a(x-y)-b(x-y)

1.1.3. Factoring by Grouping (4 terms)

1.1.3.1. Find GCF between two pairs

1.1.3.1.1. Example: x^3-6x^2+10x-60--->=x^2(x-6)+10(x-6)

1.2. Quadratic Equation

1.2.1. Completing the square

1.2.1.1. convert standard form to vertex form

1.2.1.1.1. factor all the terms by the a(ex.2s^2+4d+4=2(x^2+2x+2)

1.2.2. Quadratic formula (only used in standard form)

1.2.2.1. solving the quadratic equation standard form

1.2.2.1.1. -b+/-√ b^2-4ac divided by 2a

2. Expanding

2.1. Expanding Different Types

2.1.1. Product of sum and differences (No Middle term)(Similar to the differences of square in factoring)

2.1.1.1. (a+b)(a-b)=a^2-b^2

2.1.2. Perfect Square trinominals (Similar to factoring perfect square trinominals but expanding)

2.1.2.1. (a+b)^2= a^2+ 2ab+b^2

2.1.2.2. (a-b)^2= a^2-2ab+b^2

2.1.3. Expanding Binominals

2.1.3.1. Method (F)irst(O)utside(I)nside(L)

2.1.3.1.1. (a+b)(c+d)=ac+ad+bc+bd