Đáp án: + Giải thích các bước giải:

`c)`

`(x^2-9)^2 - (x+3)(x-3)(x^2+9)`

`= x^4 - 18x^2 + 81 - (x+3)(x-3)(x^2+9)`

`= x^4 - 18x^2 + 81 - x^4 + 81`

`= (x^4-x^4)-18x^2+(81+81)`

`= -18x^2 + 162`

`d)`

`(x^2+x-3)(x^2-x+3)`

`= x^2x^2 + x^2(-x) + x^2 * 3 + x^3 + x(-x) + x*3-3x^2-3(-x)-3*3`

`= x^4 - x^2 + 6x - 9`

*Áp dụng :

`(a+b)(x+y+z)=ax+ay+az+bx+by+bz`

Câu `6` :

`a)`

`4x(3x-7)-6(2x^2-5x+1)=12`

`⇔ 12x^2 - 28x - 6(2x^2-5x+1) = 12`

`⇔ 12x^2 - 28x - 12x^2 + 30x - 6 = 12`

`⇔ (12x^2-12x^2)+(30x-28x)-6=12`

`⇔ 2x - 6 = 12`

`⇔ 2x = 18`

`⇔ x = 9`

Vậy `S = {9}`

`b)`

`(5x+3)(4x-1)+(10x-7)(-2x+3)=27`

`⇔ 20x^2 + 7x - 3 +(10x-7)(-2x+3) = 27`

`⇔ 20x^2 + 7x - 3- 20x^2 + 44x - 21 = 27`

`⇔ (20x^2-20x^2) + (7x+44x) - (21 + 3) = 27`

`⇔ 51x - 24 = 27`

`⇔ 51x = 51`

`⇔ x = 1`

Vậy `S = {1}`

`c)`

`(8x-5)(3x+2)-(12x+7)(2x-1)=17`

`⇔ 24x^2 + x - 10 - (12x+7)(2x-1) = 17`

`⇔ 24x^2 + x - 10 - 24x^2 - 2x +7 = 17`

`⇔ (24x^2-24x^2)+(x-2x)-(10-7) = 17`

`⇔ -x - 3 = 17`

`⇔ -x = 20`

`⇔ x = -20`

Vậy `S = {-20}`

`d)`

`(5x+9)(6x-1)-(2x-3)(15x+1)=-190`

`⇔ 30x^2 + 49x - 9 - (2x-3)(15x+1) = -190`

`⇔ 30x^2 + 49x - 9 - 30x^2 + 43x + 3 = -190`

`⇔ (30x^2-30x^2)+(49x+43x)-(9-3) = -190`

`⇔ 92x - 6 = -190`

`⇔ 92x = -184`

`⇔ x = -2`

Vậy `S = {-2}`

`c)(x^2-9)^2-(x+3)(x-3)(x²+9)`

`=(x^2-9)^2-(x^2-9)(x^2+9)`

`=(x^2-9)[(x^2-9)-(x^2+9)]`

`=(x^2-9)(x^2-9-x^2-9)`

`=-18(x^2-9)`

`=-18x^2+162`

`d)(x²+x-3)(x²-x+3)`

`=[x²+(x-3)][x²-(x-3)]`

`=(x^2)^2-(x-3)^2`

`=x^4-(x²-6x+9)`

`=x^4-x²+6x-9`

`6.`

`a)4x(3x-7)-6(2x²-5x+1)=12`

`⇔12x²-28x-12x²+30x-6=12`

`⇔(12x²-12x²)+(-28x+30x)-6=12`

`⇔2x-6=12`

`⇔2x=12+6`

`⇔2x=18`

`⇔x=18:2`

`⇔x=9`

Vậy `x=9`

`b)(5x+3)(4x-1)+(10x-7)(-2x+3)=27`

`⇔20x²-5x+12x-3-20x²+30x+14x-21=27`

`⇔(20x²-20x²)+(-5x+12x+30x+14x)+(-3-21)=27`

`⇔51x-24=27`

`⇔51x=27+24`

`⇔51x=51`

`⇔x=51:51`

`⇔x=1`

Vậy `x=1`

`c)(8x-5)(3x+2)-(12x+7)(2x-1)=17`

`⇔24x²+16x-15x-10-(24x²-12x+14x-7)=17`

`⇔24x²+16x-15x-10-24x²+12x-14x+7=17`

`⇔(24x²-24x²)+(16x-15x+12x-14x)+(-10+7)=17`

`⇔-x-3=17`

`⇔-x=17+3`

`⇔-x=20`

`⇔x=-20`

Vậy `x=-20`

`d)(5x+9)(6x-1)-(2x-3)(15x+1)=-190`

`⇔30x²-5x+54x-9-(30x²+2x-45x-3)=-190`

`⇔30x²-5x+54x-9-30x²-2x+45x+3=-190`

`⇔(30x²-30x²)+(-5x+54x-2x+45x)+(-9+3)=-190`

`⇔92x-6=-190`

`⇔92x=-190+6`

`⇔92x=-184`

`⇔x=(-184):92`

`⇔x=-2`

Vậy `x=-2`