Toán Lớp 8: Phân tích đa thức thành nhân tử: a) 3x^4-12^4 b) 9a^3-12a^3+4a c) 7x^y-14xy^2+21x^2y^2 d) x^3-3x^2+3x-1-y^3 m) x^2-2x-3 n) (x^2+3x+1)(x

Question

Toán Lớp 8:  Phân tích đa thức thành nhân tử: a) 3x^4-12^4 b) 9a^3-12a^3+4a c) 7x^y-14xy^2+21x^2y^2 d) x^3-3x^2+3x-1-y^3 m) x^2-2x-3 n) (x^2+3x+1)(x^2+3x+2)-6 o)x^4+64

hienchaudiem · Answer

a)3x^4-12x^4   =3x^4(1-4)   =3x^4(1^2-2^2)   =3x^4(1+2)(1-2)   b)  9a^3-12a^3+4a     =3a(3a^2-4a^2+4/3)

cobexinhdep · Answer

Lời giải và giải thích chi tiết:    $ a.3x^{4}-12^{4}$   $= 3(x^{4}-4^{4})$   $= 3(x&sup2;-4)(x&sup2;+4)$   $= 3(x-2)(x+2)(x&sup2;+4)$   $b.9a&sup3;-12a&sup2;+4a$   $= a(9a&sup2;-12a+4)$   $= a(3a-2)&sup2;$   $c.7x&sup2;y-14xy&sup2;+21x&sup2;y&sup2;$   $=7xy(x-2y+3xy)$   $d.x&sup3;-3x&sup2;+3x-1-y&sup3;$   $=(x-1)&sup3;-y&sup3;$   $=(x-1-y)((x-1)&sup2;+y(x-1)+y&sup2;)$   $=(x-1-y)(x&sup2;-2x-1+xy-y+y&sup2;)$   $m.x&sup2;-2x-3$   $=x&sup2;-3x+x-3$   $=x(x-3)+(x-3)$   $=(x+1)(x-3)$   $n.(x&sup2;+3x+1)(x&sup2;+3x+2)-6$   $=(x&sup2;+3x+1)(x&sup2;+3x+1+1)-6$    Đặt y= $x&sup2;+3x+1$ , ta c&oacute;:    $&hArr;y(y+1)-6$   $=y&sup2;+y-6$   $=y&sup2;+3y-2y-6$   $=y(y+3)-2(y+3)$   $=(y-2)(y+3)$    Thay  $x&sup2;+3x+1$  v&agrave;o y ta được:    $&hArr;(x&sup2;+3x+1-2)(x&sup2;+3x+1+3)$   $=(x&sup2;+3x-1)(x&sup2;+3x+4)$