第1个回答 2013-01-03
1. (2x+y)^2-(x+2y)^2=(2x+y+x+2y)*(2x+y-x-2y)=3(x+y)(x-y)
2. (p-4)(p+1)+3p=p^2-4p+p-4+3p=p^2-4=(p-2)(p+2)
3. 3ax^2-3ay2=3a(x^2-y^2)=3a(x+y)(x-y)
4. 12a(x^2+y^2)-18b(x^2+y^2)=6(2a-3b)(x^2+y^2)
5. -a^5+a=-a(a^4-1)=-a(a^2+1)(a^2-1)=-a(a^2+1)(a-1)(a+1)
6. 3(m+n)^2-27n^2=3(m+n+3n)(m+n-3n)=3(m+4n)(m-2n)
7. 25(x+y)^2-9(x-y)^2=(5x+5y)^2-(3x-3y)^2=(5x+5y-3x+3y)(5x+5y+3x-3y)=4(x+4y)(4x-y)
πR1^2+πR2^2+πR3^2=3.14(4*4+8*8+10*10)=565.2
希望可以帮到你。
第2个回答 2013-01-03
1)(2x+y)^2-(x+2y)^2=(2x+y+x+2y)(2x+y-(x+2y))=(3x+3y)(x-y)=3(x-y)(x+y)
2)(p-4)(p+1)+3p=(p-1-3)(p+1)=(p-1)(p+1)-3p-3+3p=p²-4=(p-2)(p+2
3)3ax^2-3ay2=3a(x²-y²)=3a(x-y)(x+y)
4)12a(x^2+y^2)-18b(x^2+y^2)=(12a-18b)(x²+y²)=6(2a-3b)(x²+y²)
5)-a^5+a=a(1-a^4)=a(1+a²)(1-a²)=a(1+a)(1+a²)(1-a)
6)3(m+n)^2-27n^2=3((m+n)²-(3n)²)=3(m+n+3n)(m+n-3n)=3(m+4n)(m-2n)
7) 25(x+y)^2-9(x-y)^2=(5(x+y))²-(3(x-y))²=(5x+5y+3x-3y)(5x+5y-3x+3y)=4(4x+y)(x-4y)