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# 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

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

### 2 Answers

- wkho28Lv 71 decade agoFavorite 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