300501西门子:数学.题目

1.X^4-8X^2+16 =(X^2-4)^2=(X+2)(X-2)
2. X^2-9Y^2+6X+9 =(X^2+6X+9)-9Y^2=(X+3)^2-9Y^2=(X+3Y+3)(X-3Y+3)
3.X^2-9Y^2+6X-18Y =(X+3Y)(X-3Y)+6(X-3Y)=(X-3Y)(X+3Y+6)
4. 4(X+2Y)^2-25(X-Y)^2 =[2(X+2Y)+5(X-Y)][2(X+2Y)-5(X-Y)]=(7X-3Y)(7Y-3X)
5. 5(X-Y)^2-20(X-Y)+20 =5[(X-Y)^2-4(X-Y)+4]
=5(X-Y-4)^2

1. =（X^2-4）^2=(X+2)^2(X-2)^2
2. =(X^2+6X+9）-9Y^2= （X+3)^2 -9Y^2=(X+3+3Y)(X+3-3Y)
3. =(X^2-9Y^2)+(6X-18Y)=(X+3Y)(X-3Y) +6(X-3Y) =(X-3Y)(X+3Y+6)
4. =4(X^2+4XY+4Y^2) -25(X^2-2XY+Y^2)=4X^2+16XY+16Y^2-25X^2+50XY-25Y^2=-21X^2+66XY-9Y^2=-3（7X^-22XY+3Y^2）=-3(X+3Y)(7X+Y)
第五题抄错了吧？

答案(望采纳)

1.X^4-8X^2 考16 =(X^2-4)^2=(X 2)(X-2)2. X^2-9Y^2 6X 9 =(X^2 6X 9)-9Y^2=(X 3)^2-9Y^2=(X 3Y 3)(X-3Y 3)3.X^2-9Y^2 6X-18Y =(X 3Y)(X-3Y) 6(X-3Y)=(X-3Y)(X 3Y 6)4. 4(X 2Y)^2-25(X-Y)^2 =[2(X 2Y) 5(X-Y)][2(X 2Y)-5(X-Y)]=(7X-3Y)(7Y-3X)5. 5(X-Y)^2-20(X-Y) 20 =5[(X-Y)^2-4(X-Y) 4]=5(X-Y-4)^2