利用平方差公式计算 急(1) (x-1/2)(x+1/2)(x^2+1/4)(2) (根号2m+根号3n)(根号2m-根号3n)(3) (m-1/3)(m^2+1/9)(m+1/3)(4) (2x+1)(2x-1)-1(5) (-2x-1)(1-2x)-(3-2x)(2x+3)
问题描述：
利用平方差公式计算 急
(1) (x-1/2)(x+1/2)(x^2+1/4)
(2) (根号2m+根号3n)(根号2m-根号3n)
(3) (m-1/3)(m^2+1/9)(m+1/3)
(4) (2x+1)(2x-1)-1
(5) (-2x-1)(1-2x)-(3-2x)(2x+3)
答
(1) (x-1/2)(x+1/2)(x^2+1/4)=(X^2-1/4)(X^+1/4)=X^4-1/16
(2) (根号2m+根号3n)(根号2m-根号3n)
(3) (m-1/3)(m^2+1/9)(m+1/3)=m^4-1/81
(4) (2x+1)(2x-1)-1=4x^2(
5) (-2x-1)(1-2x)-(3-2x)(2x+3)=16x^2+(4x^2-3)^2
答
(1)
(x-1/2)(x+1/2)(x²+1/4)
=(x²-1/4)(x²+1/4)
=x⁴-1/16
(2)
(√2m+√3n)(√2m-√3n)
=2m²-3n²
(3)
(m-1/3)(m²+1/9)(m+1/3)
=(m²-1/9)(m²+1/9)
=m⁴-1/81
(4)
(2x+1)(2x-1)-1
=4x²-1-1
=4x²-2
(5)
(-2x-1)(1-2x)-(3-2x)(2x+3)
=4x²-1-(9-4x²)
=4x²-1-9+4x²
=8x²-10
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