Question

用平方差公式计算

①(x-1)(x+1)(x的平方+1)(x的四次方+1)

②(2+3的m次方)(2-3的m次方)
③(1/4)x的平方+(y+1/2 x)(y-1/2 x)

Answer 1

①(x-1)(x+1)(x的平方+1)(x的四次方+1)
=﹙X²﹣1﹚(x的平方+1)(x的四次方+1)
=(x的四次方-1)(x的四次方+1)
=x的八次方-1
②(2+3的m次方)(2-3的m次方)
=2²﹣﹙3的m次方﹚²
=4-3的2m次方
③(1/4)x的平方+(y+1/2 x)(y-1/2 x)
=(1/4)x的平方+y²-1/4 x²
=Y²

Answer 2

①(x-1)(x+1)(x^2+1)(x^4+1)=(x^2-1)(x^2+1)(x^4+1)=(x^4-1)(x^4+1)=x^8-1
②(2+3^m)(2-3^m)=4-3^2m=4-9^m
③(1/4)x^2+(y+1/2x)(y-1/2x)=(1/4)x^2+y^2-(1/4)x^2=y^2