数学计算题因式分解
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9a²-b²=(3a-b)(3a+b)
-1/4x²y²+0.09=(0.3-½xy)(0.3+½xy)
(m-n)²-1=(m-n-1)(m-n+1)
4x²-(x-y)²=(2x-x+y)(2x+x-y)=(x+y)(3x+y)
-(a+b)²+(2a-3b)²=(2a-3b-a-b)(2a-3b+a+b)=(a-4b)(3a-2b)
49(x-2)²-25(x-3)²=(7x-14-5x+15)(7x-14+5x-15)=(2x+1)(12x-29)
101²-99²=(101-99)(101+99)=2x200=400
1.22²x9-133²x4=(1.22×3-1.33×2)(1.22x3+1.33x2)=(3.66-2.66)(3.66+2.66)=6.32
1000²/(252²-248²)=1000²/(252-248)(252-248)=1000²/500x4=500
(1-1/2²)(1-1/3²)(1-1/4²).....(1-1/100²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).....(1-1/100)(1+1/100)
=1/2x3/2x2/3x4/3x3/4x5/4x......x98/99x100/99x99/100x101/100
=1/2x101/100
=101/200
-1/4x²y²+0.09=(0.3-½xy)(0.3+½xy)
(m-n)²-1=(m-n-1)(m-n+1)
4x²-(x-y)²=(2x-x+y)(2x+x-y)=(x+y)(3x+y)
-(a+b)²+(2a-3b)²=(2a-3b-a-b)(2a-3b+a+b)=(a-4b)(3a-2b)
49(x-2)²-25(x-3)²=(7x-14-5x+15)(7x-14+5x-15)=(2x+1)(12x-29)
101²-99²=(101-99)(101+99)=2x200=400
1.22²x9-133²x4=(1.22×3-1.33×2)(1.22x3+1.33x2)=(3.66-2.66)(3.66+2.66)=6.32
1000²/(252²-248²)=1000²/(252-248)(252-248)=1000²/500x4=500
(1-1/2²)(1-1/3²)(1-1/4²).....(1-1/100²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).....(1-1/100)(1+1/100)
=1/2x3/2x2/3x4/3x3/4x5/4x......x98/99x100/99x99/100x101/100
=1/2x101/100
=101/200
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