作业帮分别计算(x+1)(x-2)(x-3)(x-6) 和 (a+b+c+d)(a-b+c-d)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/27 19:38:18
分别计算(x+1)(x-2)(x-3)(x-6) 和 (a+b+c+d)(a-b+c-d)
分别计算(x+1)(x-2)(x-3)(x-6) 和 (a+b+c+d)(a-b+c-d)
分别计算(x+1)(x-2)(x-3)(x-6) 和 (a+b+c+d)(a-b+c-d)
(x+1)(x-2)(x-3)(x-6)
=[(x+1)(x-6)][(x-2)(x-3)]
=[(x^2-5x)-6][(x^2-5x)+6]
=(x^2-5x)^2-36
=x^4-10x^3+25x^2-36
(a+b+c+d)(a-b+c-d)
=[(a+c)+(b+d)][(a+c)-(b+d)]
=(a+c)^2-(b+d)^2
=(a^2+2ac+c^2)-(b^2+2bd+d^2)
=a^2-b^2+c^2-d^2+2ac-2bd
(x+1)(x-6) = x^2 -5x -6
(x-2)(x-3) = x^2 -5x +6
(x+1)(x-2)(x-3)(x-6) = (x^2-5x)^2 - 36
(a+b+c+d)(a+c -(b+d)) = (a+c)^2 - (b+d)^2
（x+1)(x-2)(x-3)(x-6)=
=（x+1)(x-6)(x-2)(x-3)
=(x^2-5x-6)(x^2-5x+6)
=(x^2-5x)^2-36
=x^4-10x^3+25x^2-36
(a+b+c+d)(a-b+c-d)=[(a+c)+(b+d )][(a+c)-( b+d )]
(a+b+c+d)(a-b+c-d)=[(a+c)+(b+d)][(a+c)-(b+d)]
=(a+c)(a+c)-(b-d)(b-d)
=a平方+2ac+c平方-b平方+2bd-d平方
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