a) a(b^2+c^2+bc)+b(a^2+c^2+ac)+c(b^2+a^2+ab) b)2(x^2-6x+1)^2+5(x^2-6x+1)(x^2+1)+2(x^2+1)^2 c)12x^2-20x-12xy+10y+8+3y^2

0 bình luận về “a) a(b^2+c^2+bc)+b(a^2+c^2+ac)+c(b^2+a^2+ab) b)2(x^2-6x+1)^2+5(x^2-6x+1)(x^2+1)+2(x^2+1)^2 c)12x^2-20x-12xy+10y+8+3y^2”

1. Đáp án: $a)(a+b+c)(ab+bc+ac)$

                $b)6(x^2-4x+1)(x-1)^2$

                $c)(6x-3y-4)(2x-y-2)$

    

   Giải thích các bước giải:

   $a)a(b^2+c^2+bc)+b(a^2+c^2+ac)+c(b^2+a^2+ab)$

   $=ab^2+ac^2+abc+a^2b+bc^2+abc+b^2c+a^2c+abc$

   $=(a^2b+ab^2+abc)+(a^2c+abc+ac^2)+(abc+b^2c+bc^2)$

   $=ab(a+b+c)+ac(a+b+c)+bc(a+b+c)$

   $=(a+b+c)(ab+bc+ac)$

   $b)2(x^2-6x+1)^2+5(x^2-6x+1)(x^2+1)+2(x^2+1)^2$

   $=2(x^2-6x+1)^2+(x^2-6x+1)(x^2+1)+4(x^2-6x+1)(x^2+1)+2(x^2+1)^2$

   $=(x^2-6x+1)[2(x^2-6x+1)+(x^2+1)]+2(x^2+1)[2(x^2-6x+1)+(x^2+1)]$

   $=[2(x^2-6x+1)+(x^2+1)][(x^2-6x+1)+2(x^2+1)]$

   $=(2x^2-12x+2+x^2+1)(x^2-6x+1+2x^2+2)$

   $=(3x^2-12x+3)(3x^2-6x+3)$

   $=3(x^2-4x+1).3(x^2-2x+1)$

   $=6(x^2-4x+1)(x-1)^2$

   $c)12x^2-20x-12xy+10y+8+3y^2$

   $=12x^2-6xy-8x-6xy+3y^2+4y-12x+6y+8$

   $=(12x^2-6xy-8x)-(6xy-3y^2-4y)-(12x-6y-8)$

   $=2x(6x-3y-4)-y(6x-3y-4)-2(6x-3y-4)$

   $=(6x-3y-4)(2x-y-2)$

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