3.3多项式的乘法 计算:
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/08 19:10:21
3.3多项式的乘法 计算:
(1)(a+b)(a^2-b^2) (2)(x-y)(xy-1)(3)(2x-1)(4x^2+2x+1) (4)(x-1)(x^2+x)
(1)(a+b)(a^2-b^2) (2)(x-y)(xy-1)(3)(2x-1)(4x^2+2x+1) (4)(x-1)(x^2+x)
(1)(a+b)(a²-b²)
=a×(a²-b²)+b(a²-b²)
=a×a²-a×b²+b×a²-b×b²
=a³-ab²+a²b-b³
(2)(x-y)(xy-1)
=x(xy-1)-y(xy-1)
=x²y-x-xy²+y
(3)(2x-1)(4x²+2x+1)
=8x³+4x²+2x-4x²-2x-1
=8x³-1
(4)(x-1)(x²+x)
=x³+x²-x²-x
=x³-x
=a×(a²-b²)+b(a²-b²)
=a×a²-a×b²+b×a²-b×b²
=a³-ab²+a²b-b³
(2)(x-y)(xy-1)
=x(xy-1)-y(xy-1)
=x²y-x-xy²+y
(3)(2x-1)(4x²+2x+1)
=8x³+4x²+2x-4x²-2x-1
=8x³-1
(4)(x-1)(x²+x)
=x³+x²-x²-x
=x³-x