標題:
ch...............3
factorize 42.x^2-4m^2n^2 44.x^8-16 32.4a^2-4a+1 34.25y^2-10y+1 36.4x^2-44x+121 我要步驟答案 38.16x^2-24x+9 40.4a^2+12ab+9b^2 42.20m^2+20mn+5n^2 44.8a^2+40ab+50b^2
最佳解答:
x2-4m2n2 =(x)^2-(2mn)^2 =(x-2mn)(x+2mn) （用了恆等式(a2-b2=(a+b)(a-b))） x^8-16 =(x^4)2-42 =(x^4-4)(x^4+4) =(x2-2)(x2+2)(x^4+4) 4a2-4a+1 =(2a)2-2(2a)+1 =(2a-1)2 25y2-10y+1 =(5y)2-2(5y)+12-----because1=12=13=1^n =(5y-1)2 4x2-44x+121 =(2x)2-2(2x)(11)+112 2x↘-11 2x↗-11 ---------------- -22x-22x=44x=2(2x)(11) =(2x-11)2 16x2-24x+9 =(4x)2-2(4x)(3)+32 4x↘-3 4x↗-3 ------------- -12x-12x=-24x=-2(4x)(3) =(4x-3)2 4a2+12ab+9b2 =(2a)2+2(2a)(3b)+(3b)2 2a↘3b 2a↗3b ---------- 6b+6b=2(2a)(3b) =(2a+3b)2 20m2+20mn+5n2 =5(4m2+4mn+n2) =5[(2m)2+2(2m)(n)+n2) 2m↘n 2m↗n --------- 2mn+2mn=2(2m)(n) =5(2m+n)2 8a2+40ab+50b2 =2(4a2+20ab+25b2) =2[(2a)2+2(2a)(5b)+(5b)2] 2a↘5b 2a↗5b --------- 10ab+10ab=2(2a)(5b) =2(2a+5b)2
其他解答:
42.x^2-4m^2n^2 =(x)^2-(2mn)^2 =(x-2mn)(x+2mn)// 44.x^8-16 =(x^4)^2-4^2 =(x^4-4)(x^4+4) =(x^2-2)(x^2+2)(x^4+4)// 32.4a^2-4a+1 =(2a)^2-2(2a)+1 =(2a-1)^2// 34.25y^2-10y+1 =(5y)^2-2(5y)+1^2 =(5y-1)^2// 36.4x^2-44x+121 =(2x)^2-2(2x)(11)+11^2 =(2x-11)^2// 38.16x^2-24x+9 =(4x)^2-2(4x)(3)+3^2 =(4x-3)^2// 40.4a^2+12ab+9b^2 =(2a)^2+2(2a)(3b)+(3b)^2 =(2a+3b)^2// 42.20m^2+20mn+5n^2 =5(4m^2+4mn+n^2) =5[(2m)^2+2(2m)(n)+n^2) =5(2m+n)^2// 44.8a^2+40ab+50b^2 =2(4a^2+20ab+25b^2) =2[(2a)^2+2(2a)(5b)+(5b)^2] =2(2a+5b)^2//
ch...............3
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發問:factorize 42.x^2-4m^2n^2 44.x^8-16 32.4a^2-4a+1 34.25y^2-10y+1 36.4x^2-44x+121 我要步驟答案 38.16x^2-24x+9 40.4a^2+12ab+9b^2 42.20m^2+20mn+5n^2 44.8a^2+40ab+50b^2
最佳解答:
x2-4m2n2 =(x)^2-(2mn)^2 =(x-2mn)(x+2mn) （用了恆等式(a2-b2=(a+b)(a-b))） x^8-16 =(x^4)2-42 =(x^4-4)(x^4+4) =(x2-2)(x2+2)(x^4+4) 4a2-4a+1 =(2a)2-2(2a)+1 =(2a-1)2 25y2-10y+1 =(5y)2-2(5y)+12-----because1=12=13=1^n =(5y-1)2 4x2-44x+121 =(2x)2-2(2x)(11)+112 2x↘-11 2x↗-11 ---------------- -22x-22x=44x=2(2x)(11) =(2x-11)2 16x2-24x+9 =(4x)2-2(4x)(3)+32 4x↘-3 4x↗-3 ------------- -12x-12x=-24x=-2(4x)(3) =(4x-3)2 4a2+12ab+9b2 =(2a)2+2(2a)(3b)+(3b)2 2a↘3b 2a↗3b ---------- 6b+6b=2(2a)(3b) =(2a+3b)2 20m2+20mn+5n2 =5(4m2+4mn+n2) =5[(2m)2+2(2m)(n)+n2) 2m↘n 2m↗n --------- 2mn+2mn=2(2m)(n) =5(2m+n)2 8a2+40ab+50b2 =2(4a2+20ab+25b2) =2[(2a)2+2(2a)(5b)+(5b)2] 2a↘5b 2a↗5b --------- 10ab+10ab=2(2a)(5b) =2(2a+5b)2
其他解答:
42.x^2-4m^2n^2 =(x)^2-(2mn)^2 =(x-2mn)(x+2mn)// 44.x^8-16 =(x^4)^2-4^2 =(x^4-4)(x^4+4) =(x^2-2)(x^2+2)(x^4+4)// 32.4a^2-4a+1 =(2a)^2-2(2a)+1 =(2a-1)^2// 34.25y^2-10y+1 =(5y)^2-2(5y)+1^2 =(5y-1)^2// 36.4x^2-44x+121 =(2x)^2-2(2x)(11)+11^2 =(2x-11)^2// 38.16x^2-24x+9 =(4x)^2-2(4x)(3)+3^2 =(4x-3)^2// 40.4a^2+12ab+9b^2 =(2a)^2+2(2a)(3b)+(3b)^2 =(2a+3b)^2// 42.20m^2+20mn+5n^2 =5(4m^2+4mn+n^2) =5[(2m)^2+2(2m)(n)+n^2) =5(2m+n)^2// 44.8a^2+40ab+50b^2 =2(4a^2+20ab+25b^2) =2[(2a)^2+2(2a)(5b)+(5b)^2] =2(2a+5b)^2//
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