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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: Phân tích đa thức thành nhân tử: a) ab (a-b) + bc (b-c) +ca (c- a); b) (a+ b+c)^3 – a^3 – b^3 – c^3; c) 4a^2b^2 – (a^2 + b^2 – c^2)2 ;

Tháng Hai 2, 2023 Toán học 2 Comments 0 views

Toán Lớp 8: Phân tích đa thức thành nhân tử: a) ab (a-b) + bc (b-c) +ca (c- a); b) (a+ b+c)^3 – a^3 – b^3 – c^3; c) 4a^2b^2 – (a^2 + b^2 – c^2)2 ;

Comments ( 2 )

  1. huongtructram
    huongtructram
    2 Tháng Hai, 2023 at 4:13 chiều
    Reply
    a)ab(a-b)+bc(b-c)+ca(c-a)
    =ab(a-b)+b²c-bc²+ac²-a²c
    =ab(a-b)+(ac²-bc²)-(a²c-b²c)
    =ab(a-b)+c²(a-b)-c(a²-b²)
    =ab(a-b)+c²(a-b)-c(a+b)(a-b)
    =(a-b)[ab+c²-c(a+b)]
    =(a-b)(ab+c²-ac-bc)
    =(a-b)[(ab-ac)-(bc-c²)]
    =(a-b)[a(b-c)-c(b-c)]
    =(a-b)(b-c)(a-c)
    b)(a+b+c)³-a³-b³-c³
    =[(a+b+c)³-a³]-(b³+c³)
    =(a+b+c-a)[(a+b+c)²+a(a+b+c)+a²]-(b+c)(b²-bc+c²)
    =(b+c){[(a+b)+c]²+a²+ab+ac+a²}-(b+c)(b²-bc+c²)
    =(b+c)[(a+b)²+2c(a+b)+c²+a²+ab+ac+a²]-(b+c)(b²-bc+c²)
    =(b+c)[(a+b)²+2c(a+b)+c²+a²+ab+ac+a²-(b²-bc+c²)]
    =(b+c)(a²+2ab+b²+2ac+2bc+c²+a²+ab+ac+a²-b²+bc-c²)
    =(b+c)[(a²+a²+a²)+(b²-b²)+(c²-c²)+(2ab+ab)+(2ac+ac)+(2bc+bc)]
    =(b+c)(3a²+3ab+3ac+3bc)
    =3(b+c)(a²+ab+ac+bc)
    =3(b+c)[a(a+b)+c(a+b)]
    =3(a+b)(b+c)(a+c)
    c)4a²b²-(a²+b²-c²)²
    =(2ab)²-(a²+b²-c²)²
    =(2ab+a²+b²-c²)[2ab-(a²+b²-c²)]
    =(2ab+a²+b²-c²)(2ab-a²-b²+c²)
    =[(a²+2ab+b²)-c²][c²-(a²-2ab+b²)]
    =[(a+b)²-c²][c²-(a-b)²]
    =(a+b+c)(a+b-c)(c+a-b)(c-a+b)

  2. aivilanlan
    aivilanlan
    2 Tháng Hai, 2023 at 4:13 chiều
    Reply
    Giải đáp:
    a)ab(a-b)+bc(b-c)+ca(c-a)
    =ab(a-b)+b^2c-bc^2+c^2a-ca^2
    =ab(a-b)+c^2(a-b)-c(a^2-b^2)
    =ab(a-b)+c^2(a-b)-c(a-b)(a+b)
    =(a-b)(ab+c^2-ac-bc)
    =(a-b)[a(b-c)-c(b-c)]
    =(a-b)(b-c)(a-c)
    b)(a+b+c)^3-a^3-b^3-c^3
    =(a+b)^3+3c(a+b)(a+b+c)+c^3-a^3-b^3-c^3
    =a^3+3ab(a+b)+b^3+3c(a+b)(a+b+c)+c^3-a^3-b^3-c^3
    =3ab(a+b)+3c(a+b)(a+b+c)
    =3(a+b)(ab+ca+cb+c^2)
    =3(a+b)[a(b+c)+c(b+c)]
    =3(a+b)(b+c)(c+a)
    c)4a^2b^2-(a^2+b^2-c^2)^2
    =(2ab)^2-(a^2+b^2-c^2)^2
    =(2ab-a^2-b^2+c^2)(2ab+a^2+b^2-c^2)
    =[c^2-(a-b)^2][(a+b)^2-c^2]
    =(c-a+b)(c+a-b)(a+b-c)(a+b+c).

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222-9+11+12:2*14+14 = ? ( )

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