Question

因式分解数学题 求答案和过程

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

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

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

⑤429²×2-171²×2
=2(429²-171²)
=2(429+171)(429-171)
=2×600×358
=429600

⑥1000²/252²-248²
=1000²/(252+248)(252-248)
=1000²/500×4
=500

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

追问

啊哈 又是你

Answer 2

①16m^-n^4缺点啥
②16（a-b）²-9（a+b)²=（4a-4b）^2-(3a+3b)^2=(4a-4b+3a+3b)(4a-4b-3a-3b)=(7a-b)(a-7b)
③x^5y-xy=xy(x^4-1)=xy(x+1)(x-1)(x^2+1)
④2012²-2011²=(2012+2011)(2012-2011)=4023
⑤429²×2-171²×2=2(429+171)(429-171)=2*600*258=309600
⑥1000²/252²-248²下面是不是有括号？1000²/（252²-248²）=1000²/（252+248）（252-248）=1000²/（500*4）=500
⑦（50又1/11）²-（49又10/11）²=(551/11+549/11)(551/11-549/11)=100*2/11=200/11