Question

(2x-3y)平方(2x+3y)平方(4x平方+9y平方)平方

简便运算：
1. (2x-3y)平方(2x+3y)平方(4x平方+9y平方)平方
2. (x-1)(x+1)(x+3)(x+5)
3. x(x+1)(x+2)(x+3)
4. (x+1)(x+2)(x+3)(x+4)
注：2.3.4是同一类型的

Answer 1

1. (2x-3y)平方(2x+3y)平方(4x平方+9y平方)平方
=[(2x-3y)(2x+3y)](4x平方+9y平方)平方
=[4x^2-9y^2][4x^2+9y^2]
=16x^4-81y^4

2. (x-1)(x+1)(x+3)(x+5)
=[(x-1)(x+5)][(x+1)(x+3)]
=[x^2+4x-5][x^2+4x+3]

=[x^2+4x]^2-2(x^2+4x)-15

=x^4+8x^3+16x^2-2x^2-8x-15

=x^4+8x^3+14x^2-8x-15

3. x(x+1)(x+2)(x+3)
=[x(x+3)][(x+1)(x+2)]

=[x^2+3x][x^2+3x+2]
=[x^2+3x]+2[x^2+3x]
=x^4+6x^3+9x^2+2x^2+6x
=x^4+6x^3+11x^2+6x

4. (x+1)(x+2)(x+3)(x+4)
=[(x+1)(x+4)][(x+2)(x+3)]
=[x^2+5x+4][x^2+5x+6]

=[x^2+5x]^2+10[x^2+5x]+24

=x^4+10x^3+25x^2+10x^2+50x+24

=x^4+10x^3+35x^2+50x+24

Answer 2

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