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How do I expand quadratics?

By Lee Mansfield on the 11th of June, 2012

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    Expand & Factorize Quadratic Expressions

    Expanding Quadratic Expressions

    Quadratic expressions are algebraic expressions where the variable has a power of 2.

    For example: x2+3x+4

    To expand quadratic equations, use the FOIL (First, Outside, Inside, Last) method.

    First Outside Inside Last

    Example 1

    Expand (x+3)(x+2)

    Answer (without using FOIL):

     

    (x+3)(x+2)=x(x+2)+3(x+2)=x2+2x+3x+6=x2+5x+6

    Answer (with using FOIL):

     

    (x+3)(x+2)=x2+2x+3x+6=x2+5x+6

    Example 2

     

    (x+4)(x2)=x22x+4x8=x2+2x8

    Example 3

     

    (2x+5)(3x8)=6x216x+15x40=6x2x40

    Questions - Expand Using FOIL

    Q1. (x+6)(x+5)
    Q2. (x5)(x4)
    Q3. (2x+5)(6x2)

    Answers:

    A1. x2+11x+30
    A2. x29x+20
    A3. 12x2+26x10

    Perfect Squares

    (x+a)2=x2+2ax+a2(xa)2=x22ax+a2

    Example 4

     

    (x+5)2=(x+5)(x+5)=x2+10x+25

    Example 5

     

    (x3)2=(x3)(x3)=x26x+9

    Questions - Expand These Perfect Squares

    Q1. (x+7)2
    Q2. (2x+5)2

    Answers:

    A1. x2+14x+49
    A2. 4x2+20x+25

    Difference of Squares

    (x+a)(xa)=x2a2

    Example 6

     

    (x+5)(x5)=x25x+5x25=x225

    Example 7

     

    (x3)(x+3)=x23x+3x9=x29

    Questions - Expand These Difference of Squares

    Q1. (x+7)(x7)
    Q2. (2x+5)(2x5)

    Answers:

    A1. x249
    A2. 4x225

    Factorizing Quadratic Expressions

    Factorizing is the reverse of expanding.

     


    Example 8

     

    x2+6x+5=(x+5)(x+1)

    Example 9

     

    6x2+2x20=(2x+4)(3x5)

    Questions - Factorize

    Q1. x27x8
    Q2. x2+x12

    Answers:

    A1. (x8)(x+1)
    A2. (x+4)(x3)

     

     

     

    Refine By kristen k on the 17th of January, 2013

2Simple software

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