f.1 algebraic expressions(20分)

expand the following expressions

x代表英文符號,*代表次方,eg:*2=二次方

1.(3x+2)(2-5x)

2.5x(x-3)(x+4)2x*2(x-3)

3.(x+y)*2 -(x-y)*2

Update:

4.if n is an even number,what is the sum of the next three even numbers after n?

2 Answers

Rating
  • wkho28
    Lv 7
    1 decade ago
    Favorite Answer

    expand the following expressions

    1. (3x+2)(2-5x)

    =3x(2-5x)+2(2-5x)

    =6x-15x2+4-10x

    =-15x2-4x+4

    2. [5x(x-3)(x+4)][2x2(x-3)]

    =10x3(x-3)(x+4)(x-3)

    =10x3(x+4)(x-3)(x-3)

    =10x3(x+4)(x2-6x+9)

    =10x3[x(x2-6x+9)+4(x2-6x+9)]

    =10x3(x3-6x2+9x+4x2-24x+36)

    =10x3(x3-2x2-15x+36)

    =10x6-20x5-150x4+360x3

    3. (x+y)2-(x-y)2

    =(x2+2xy+y2)-(x2-2xy+y2)

    =x2+2xy+y2-x2+2xy-y2

    =2xy+2xy

    =4xy

    Method 2: Use identity a2-b2=(a+b)(a-b)

    Put a=x+y and b=x-y

    (x+y)2-(x-y)2

    = a2-b2

    =(a+b)(a-b)

    =[(x+y)+(x-y)][(x+y)-(x-y)]

    =(x+y+x-y)(x+y-x+y)

    =(2x)(2y)

    =4xy

    4. If n is an even number, what is the sum of the next three even numbers after n?

    Next three even numbers after n are : n+2, n+4, n+6

    The sum is : (n+2)+(n+4)+(n+6)= n+2+n+4+n+6=3n+12=3(n+4)

  • 1 decade ago

    1.(3x+2)(2-5x)

    =6x+4-15x*2-10x

    =-15x*2-4x+4

    2.5x(x-3)(x+4)2x*2(x-3)

    =(5x*2-15x)(x+4)2x*2(x-3)

    =(5x*3-15x*2+20x*2-60x)2x*2(x-3)

    =(5x*3+5x*2-60x)2x*2(x-3)

    =(10x*5+10x*4-120x*3)(x-3)

    =10x*6+10x*5-120x*4-30x*5-30x*4+360x*3

    =10x*6-20x*5-150x*4+360x*3

    3.(x+y)*2 -(x-y)*2

    =[(x+y)+(x-y)][(x+y)-(x-y)]

    =[x+y+x-y][x+y-x+y]

    =2x*2y

    =4xy

    4.The sum of the next three even numbers after n

    =n+2+n+4+n+6

    =3n+12

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