1,Tính nhẩm a,61^2 b201^2 c10,1^2 2,Tính nhẩm a,199^2 b,9,9^2 3,Tính a,(a+b-c)^2 b,(x+y+z)*(x+y-z)

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1. 1. 

   a) 61^2=3721

   b) 201^2= 40401

   c) 10,1^2= 102,01

   2. 

   a) 199^2= 39601

   b) 9,9^2= 98,01

   3. 

   a) (a+b-c)^2

   = (a+b)^2 – 2(a+b)c+ c^2

   = a^2+2ab+b^2-2ac-2bc+c^2

   = a^2+b^2+c^2+2ab-2ac-2bc

   b) (x+y+z)*(x+y-z)

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

   = x^2+2xy+y^2-z^2

    

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2. Đáp án:

    

   Giải thích các bước giải:

   $61^2=(60+1)^2=60^2+2.60+1=3600+120+1=3721$

   $201^2=(200+1)^2=200^2+2.200+1=40000+400+1=40401$

   $10,1^2=(10+0,1)^2=10^2+2.10.0,1+0.1^2=100+2+0,01=102,01$

   $199^2=(200-1)^2=200^2-2.200+1=40000-400+1=39601$

   $9,9^2=(10-0,1)^2=100-2.10.0,1+0,1^2=100-2+0,01=98,01$

   3.

   $(a+b-c)^2$

   $=[(a+b)-c]^2$

   $=(a+b)^2-2.(a+b).c+c^2$

   $=a^2+2ab+b^2-2ac-2ab+c^2$

   $=a^2+b^2+c^2-2ac$

   $b,(x+y+z)(x+y-z)$

   $=[(x+y)+z][(x+y)-z]$

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

   $=x^2+2xy+y^2-z^2$

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