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F4 maths L.C.M ,h.C.F
FINF THE H.C.F AND L.C.M of the followings, 1.)6(2a-3b)^2(2a+3b)^3 and 36^a-81b^2 2.)let F(x)=x^4+4x^3-5x^2-36x-36 and g(x)=3x^3+24. a)show that(x^2+2x)^2-(3x+6)^2=x^4+4x^3-5x^2-36x-36 b)fing theH.C.F and L.C.M of f(x) and g(x) thx~
最佳解答:
Hi , I am lop , feel happy to answer your question . (1)36a^2 - 81b^2= 9(4a^2 – 9b^2)= 9(2a+3b)(3a-3b)The L.C.M. of the two expressions :L.C.M. of (6,9) × (2a-3b)^2(2a+3b)^3= 18(2a-3b)^2(2a+3b)^3 = 576a^5 + 864a^4(b) - 2592(a^3)(b^2) - 3888(a^2)(b^3) + 2916ab^4 + 4374b^5The HC.F. of the two expressions := H.C.F. of [6,9] × (2a+3b)(2a-3b)= 3(2a+3b)(2a-3b) = 12a^2 - 27b^2(2)(a) (x^2+2x)^2-(3x+6)^2= (x^2)^2 + 2(2x)(x^2) + (2x)^2 – [(3x)^2 + 2(6)(3x) +(6)^2]= x^4 + 4x^3 + 4x^2 – 9x^2 – 36x – 36= x^4 + 4x^3 - 5x^2 - 36x – 36= R.H.S.(b) g(x)= 3x^3+24= 3(x^3+8)= 3(x+2)(x^2-2x+4)f(x)= (x^2+2x)^2-(3x+6)^2= (x^2+2x+3x+6)(x^2+2x-3x-6)= (x^2+5x+6)(x^2-x-6)= (x+3)(x+2)(x-3)(x+2)= (x+3)(x-3)(x+2)^2The L.C.M. of f(x) and g(x) := 3(x+2)^2(x+3)(x-3)(x^2-2x+4) = 3x^6 + 6x^5 - 27x^4 - 30x^3 + 48x^2 - 216x - 432The H.C.F. of f(x) and g(x) := (x+2)
其他解答:
1 6(2a-3b)^2(2a+3b)^3 36a^2-81b^2 6(2a-3b)^2(2a+3b)^3 (6a-9b)(6a+9b) (2)(3)(2a-3b)^2(2a+3b)^3 (3)(3)(2a-3b)(2a+3b) H.C.F.=3(2a-3b)(2a+3b) L.C.F.=18(2a-3b)^2(2a+3b)^3 2a (x^2+2x)^2-(3x+6)^2=x^4+4x^3-5x^2-36x-36 left=x^4+4x^3+4x^2-9x^2-36x+36 left=x^4+4x^3-5x^2-36x+36 left=right 2b x^4+4x^3-5x^2-36x-36 3x^3+24 (x^2+2x)^2-(3x+6)^2 3(x^3+8) (x^2-x-6)(x^2+5x+6) 3(x+2)(x^2-2x+4) (x-3)(x+3)(x+2)^2 3(x+2)(x-2x+4) H.C.F.=(x+2) L.C.F=3(x-3)(x+3)(x+2)^2(x-2x+4)
F4 maths L.C.M ,h.C.F
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發問:FINF THE H.C.F AND L.C.M of the followings, 1.)6(2a-3b)^2(2a+3b)^3 and 36^a-81b^2 2.)let F(x)=x^4+4x^3-5x^2-36x-36 and g(x)=3x^3+24. a)show that(x^2+2x)^2-(3x+6)^2=x^4+4x^3-5x^2-36x-36 b)fing theH.C.F and L.C.M of f(x) and g(x) thx~
最佳解答:
Hi , I am lop , feel happy to answer your question . (1)36a^2 - 81b^2= 9(4a^2 – 9b^2)= 9(2a+3b)(3a-3b)The L.C.M. of the two expressions :L.C.M. of (6,9) × (2a-3b)^2(2a+3b)^3= 18(2a-3b)^2(2a+3b)^3 = 576a^5 + 864a^4(b) - 2592(a^3)(b^2) - 3888(a^2)(b^3) + 2916ab^4 + 4374b^5The HC.F. of the two expressions := H.C.F. of [6,9] × (2a+3b)(2a-3b)= 3(2a+3b)(2a-3b) = 12a^2 - 27b^2(2)(a) (x^2+2x)^2-(3x+6)^2= (x^2)^2 + 2(2x)(x^2) + (2x)^2 – [(3x)^2 + 2(6)(3x) +(6)^2]= x^4 + 4x^3 + 4x^2 – 9x^2 – 36x – 36= x^4 + 4x^3 - 5x^2 - 36x – 36= R.H.S.(b) g(x)= 3x^3+24= 3(x^3+8)= 3(x+2)(x^2-2x+4)f(x)= (x^2+2x)^2-(3x+6)^2= (x^2+2x+3x+6)(x^2+2x-3x-6)= (x^2+5x+6)(x^2-x-6)= (x+3)(x+2)(x-3)(x+2)= (x+3)(x-3)(x+2)^2The L.C.M. of f(x) and g(x) := 3(x+2)^2(x+3)(x-3)(x^2-2x+4) = 3x^6 + 6x^5 - 27x^4 - 30x^3 + 48x^2 - 216x - 432The H.C.F. of f(x) and g(x) := (x+2)
其他解答:
1 6(2a-3b)^2(2a+3b)^3 36a^2-81b^2 6(2a-3b)^2(2a+3b)^3 (6a-9b)(6a+9b) (2)(3)(2a-3b)^2(2a+3b)^3 (3)(3)(2a-3b)(2a+3b) H.C.F.=3(2a-3b)(2a+3b) L.C.F.=18(2a-3b)^2(2a+3b)^3 2a (x^2+2x)^2-(3x+6)^2=x^4+4x^3-5x^2-36x-36 left=x^4+4x^3+4x^2-9x^2-36x+36 left=x^4+4x^3-5x^2-36x+36 left=right 2b x^4+4x^3-5x^2-36x-36 3x^3+24 (x^2+2x)^2-(3x+6)^2 3(x^3+8) (x^2-x-6)(x^2+5x+6) 3(x+2)(x^2-2x+4) (x-3)(x+3)(x+2)^2 3(x+2)(x-2x+4) H.C.F.=(x+2) L.C.F=3(x-3)(x+3)(x+2)^2(x-2x+4)
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