因式分解題

2022-08-29 08:45:16 字數 935 閱讀 2801

1樓:我不是他舅

(1)(a+b)^2-(a-b)^2

=[(a+b)+(a-b)][(a+b)-(a-b)]=(a+b+a-b)(a+b-a+b)

=2a*2b

=4ab

(2)x^3+x^2y-xy^2-y^3

=x^2(x+y)-y^2(x+y)

=(x+y)(x^2-y^2)

=(x+y)^2(x-y)

(3)(5m^2+3n^2)^2-(3m^2+5n^2)^2=[(5m^2+3n^2)+(3m^2+5n^2)][(5m^2+3n^2)-(3m^2+5n^2)]

=(8m^2+8n^2)(2m^2-2n^2)=16(m^2+n^2)(m+n)(m-n)2.將一條長100cm的金色彩帶剪成兩段,恰好可以裝飾兩張大小不等的正方形油畫(不計接頭重疊部分),若兩張油畫的面積相差50cm^2,問這兩條綵帶應剪多長?

設一根xcm,另一根100-xcm,不妨設x>100-x,x>50這就是正方形的邊長

則兩個正方形邊長是x/4,(100-x)/4所以面積差=(x/4)^2-[(100-x)/4]^2=[x/4+(100-x)/4][x/4-(100-x)/4]=100*(x/2-100/4)=50

x/2-25=50/100=1/2

x=50+1=51

100-x=49

所以一根51cm,一根49cm

2樓:匿名使用者

(1)(a+b+a-b)(a+b-a+b)=2a*2b=4ab

(2)x^2(x+y)-y^2(x+y)=(x+y)(x-y)(x+y)=(x-y)(x+y)^2

(3)(5m^2+3n^2+3m^2+5n^2)(5m^2+3n^2-3m^2-5n^2)=(8m^2+8n^2)(2m^2-2n^2)=16(m^2+n^2)(m^2-n^2)=16(m^2+n^2)(m+n)(m-n)

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