3.3多项式的乘法 计算:
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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)
![3.3多项式的乘法 计算:](/uploads/image/z/19899030-30-0.jpg?t=3.3%E5%A4%9A%E9%A1%B9%E5%BC%8F%E7%9A%84%E4%B9%98%E6%B3%95+%E8%AE%A1%E7%AE%97%EF%BC%9A)
(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