Question

因式分解数学题 谢了

①16m^-n^4②16（a-b）²-9（a+b)²③x^5y-xy④2012²-2011²⑤429²×2-171²×2⑥1000²/252²-248²⑦（50又1/11）²-（49又10/11）²

Answer 1

①16m^4-n^4
=(4m²+n²)(4m²-n²)
=(4m²+n²)(2m-n)(2m+n)

②16（a-b）²-9（a+b)²
=[4（a-b）-3(a+b)]·[4（a-b）+3(a+b)]
=(4a-4b-3a-3b)(4a-4b+3a+3b)
= (a-7b)(7a-b)

③x^5y-xy=xy(x^4-1)
= xy(x²-1)(x²+1) = xy(x-1)(x+1)(x²+1)

④2012²-2011² = (2012-2011)(2012+2011) = 4023

⑤429²×2-171²×2
= 2×(429²-171²)
= 2×(429-171)(429+171) = 2×258×600=309600

⑥（分母是否是252²-248²？）
1000²/252²-248²=1000²/(252+248)(252-248)=1000²/500×4=1000/2=500

⑦（50又1/11）²-（49又10/11）²
=（50+1/11）²-（49+10/11）²
=(50+1/11-49-10/11)(50+1/11+49+10/11)
=2/11×100=200/11

Answer 2

这是什么？？怎么看不出来

Answer 3

①题目错了

追问

16m^4-n^4

追答

①16m^4-n^4
=(4m^2+n^2)(4m^2-n^2)
=(4m^2+n^2)(2m-n)(2m+n)

② 16(a-b)^2-9(a+b)^2
=[4(a-b)]^2-[3(a+b)]^2
=[4(a-b)-3(a+b)][4(a-b)+3(a+b)]

=(a-7b)(7a-b)

③x^5y-xy
=x^4(xy)

④=4023

⑤429²×2-171²×2
=(4292－1712)×2
=2580×2
=5160

⑥=1000²/(252+248)×(252-248)
=1000²/(500×4)
=1000²/(1000×2)
=1000/2
=500

望采纳