a. 7x^2-7xy-5x+5y b. x^2-6x+9-9y^2 c. 2xy+3z+6y+xz d. a^4+6a^2+9-36t^2 e. a^2+2ab+b^2-x^2+2xy-y^2 g. x^2-4x^2y^2+y^2+2xy h. 25-a^2+2ab-b

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1. Đáp án:

    

   Giải thích các bước giải:

   $a,7x^2-7xy-5x+5y$

   $=7x(x-y)-5(x-y)$

   $=(7x-5)(x-y)$

   $b,x^2-6x+9-9y^2$

   $=(x-3)^2-(3y)^2$

   $=(x-3-3y)(x-3+3y)$

   $c,2xy+3z+6y+xz$

   $=2y(x+3)+z(x+3)$

   $=(2y+z)(x+3)$

   $d,a^4+6a^2+9-36t^2$

   $=(a^2+3)-(6t)^2$

   $=(a^2+3-6t)(a^2+3+6t)$

   $e,a^2+2ab+b^2-x^2+2xy-y^2$

   $=(a+b)^2-(x-y)^2$

   $=(a+b-x+y)(a+b+x-y)$

   $g,x^2-4x^2y^2+y^2+2xy$

   $=(x+y)^2-(2xy)^2$

   $=(x+y-2xy)(x+y+2xy)$

   $=(x-y)^2(x+y)^2$

   $h,25-a^2+2ab-b^2$

   $=5^2-(a-b)^2$

   $=(5-a+b)(5+a-b)$

   $m.x^2+2xy+y^2-xz-yz$

   $=(x+y)^2-z(x+y)$

   $=(x+y)(x+y-z)$

   $n,a^3+3a^2+3a+1-a-1$

   $=(a+1)^3-(a+1)$

   $=(a+1)(a^2+2a+1-1)$

   $=(a+1)(a^2+2a)$

   $=(a+1)(a+2)a$

   Trả lời

2. a. $7x^{2}$ – 7xy -5x + 5y

   = 7x(x-y) -5(x-y)

   =(x-y) (7x-5)

   b. $x^{2}$ -6x + 9 -$9y^{2}$ 

   = $(x-3)^{2}$ – $(3y)^{2}$ 

   = (x-3-3y)(x-3+3y)

   c. 2xy + 3z +6y + xz 

   =2y(x+3) + z(x+3)

   =(x+3)((2y+z)

   d. $a^{4}$ + $6a^{2}$ + 9 – $36t^{2}$

   = $(a^{2}+ 3)^{2}$ – $(6t)^{2}$

   = ($a^{2}$ +3 -6t)($a^{2}$ +3 +6t)

   e. $a^{2}$ + 2ab + $b^{2}$ -$x^{2}$ +2xy – $y^{2}$ 

   = $(a+b)^{2}$ – $(x+y)^{2}$ 

   = (a+b-x-y)(a+b+x+y)

   g. $x^{2}$ – 4$x^{2}$ $y^{2}$ + $y^{2}$ +2xy 

   = $(x+y)^{2}$ – $(2xy)^{2}$ 

   = (x+y-2xy)(x+y+2xy)

   h.25 -$a^{2}$ + 2ab – $b^{2}$ 

   = -($a^{2}$ – 2ab + $b^{2}$ -25 )

   = -($(a-b)^{2}$  -$5^{2}$ )

   = -[(a-b-5)(a-b+5)]

   Trả lời