Bài 1 là Thu gọn hằng đẳng thức

Câu trong ảnh làm như nào các bạn ơi... $1)~4x^4-4x^2+1$ $2)~4x^2-12x+9$ $3)~36+x^2-12x$,$4)~1-10x+25x^2$ $5)~x^4+81+18x^2$ $6)~4x^2-20x+25$,$7)~8x^3-12x^2+6x-1$ $8)~x^3+3x^2y+3xy^2+y^3$ $9)~x^3-6x^2y+12xy^2-8y^3$,Bài 2: Thu gọn hằng đẳng thức,$1)~(x+1)(x^2-x+1)$ $2)~(x-1)(x^2+x+1)$ $3)~(x-2)(x^2+2x+4)$,$4)~(x+2)(x^2-2x+4)$ $5)~(x-3)(x^2+3x+9)$ $6)~(x-4)(x^2+4x+16)$,$7)~(4x-3y)(16x^2+9y^2+12xy)$ $8)~(3x-4y)(9x^2+16y^2+12xy)$,Bài 3: Thực hiện phép tính,$1)~(-x-2)^3+(2x-4)(x^2+2x+4)-x^2(x-6)$,$2)~(x-1)^3-(x+2)(x^2-2x+4)+3(x+4)(x-4)$,$3)~(x+y)(x^2-xy+y^2)+3(2x-y)(4x^2+2xy+y^2)$,$4)~(x+3y)(x^2-3xy+9y^2)+(3x-y)(9x^2+3xy+y^2)$,Bài 4: Tìm x,$1)~8x^3-12x^2+6x-1=0$ $2)~x^3-6x^2+12x-8=27$,$3)~x^2-8x+16=5(4-x)^3$ $4)~(2-x)^3=6x(x-2)$,$5)~(x+1)^3-(x-1)^3-6(x-1)^2=-10$ $6)~(3-x)^3-(x+3)^3=36x^2-54x$

Question

Bài 1 là Thu gọn hằng đẳng thức

Câu trong ảnh làm như nào các bạn ơi... $1)~4x^4-4x^2+1$ $2)~4x^2-12x+9$ $3)~36+x^2-12x$,$4)~1-10x+25x^2$ $5)~x^4+81+18x^2$ $6)~4x^2-20x+25$,$7)~8x^3-12x^2+6x-1$ $8)~x^3+3x^2y+3xy^2+y^3$ $9)~x^3-6x^2y+12xy^2-8y^3$,Bài 2: Thu gọn hằng đẳng thức,$1)~(x+1)(x^2-x+1)$ $2)~(x-1)(x^2+x+1)$ $3)~(x-2)(x^2+2x+4)$,$4)~(x+2)(x^2-2x+4)$ $5)~(x-3)(x^2+3x+9)$ $6)~(x-4)(x^2+4x+16)$,$7)~(4x-3y)(16x^2+9y^2+12xy)$ $8)~(3x-4y)(9x^2+16y^2+12xy)$,Bài 3: Thực hiện phép tính,$1)~(-x-2)^3+(2x-4)(x^2+2x+4)-x^2(x-6)$,$2)~(x-1)^3-(x+2)(x^2-2x+4)+3(x+4)(x-4)$,$3)~(x+y)(x^2-xy+y^2)+3(2x-y)(4x^2+2xy+y^2)$,$4)~(x+3y)(x^2-3xy+9y^2)+(3x-y)(9x^2+3xy+y^2)$,Bài 4: Tìm x,$1)~8x^3-12x^2+6x-1=0$ $2)~x^3-6x^2+12x-8=27$,$3)~x^2-8x+16=5(4-x)^3$ $4)~(2-x)^3=6x(x-2)$,$5)~(x+1)^3-(x-1)^3-6(x-1)^2=-10$ $6)~(3-x)^3-(x+3)^3=36x^2-54x$

Accepted Answer

{"userId":5421845,"userName":"Lê Lan"}

Bài 1

1) 4x4−4x2+14x^4 - 4x^2 + 14x4−4x2+1

Dạng: a2−2ab+b2=(a−b)2a^2 - 2ab + b^2 = (a-b)^2a2−2ab+b2=(a−b)2
Viết lại: (2x2)2−2(2x2)(1)+12(2x^2)^2 - 2(2x^2)(1) + 1^2(2x2)2−2(2x2)(1)+12
→ (2x2−1)2(2x^2 - 1)^2(2x2−1)2

2) 4x2−12x+94x^2 - 12x + 94x2−12x+9

Dạng: a2−2ab+b2=(a−b)2a^2 - 2ab + b^2 = (a-b)^2a2−2ab+b2=(a−b)2
Viết lại: (2x)2−2(2x)(3)+32(2x)^2 - 2(2x)(3) + 3^2(2x)2−2(2x)(3)+32
→ (2x−3)2(2x - 3)^2(2x−3)2

3) 36+x2−12x36 + x^2 - 12x36+x2−12x

Sắp xếp: x2−12x+36x^2 - 12x + 36x2−12x+36
Dạng: (x−6)2(x - 6)^2(x−6)2

4) 1−10x+25x21 - 10x + 25x^21−10x+25x2

Viết lại: 25x2−10x+125x^2 - 10x + 125x2−10x+1
Dạng: (5x−1)2(5x - 1)^2(5x−1)2

5) x4+81+18x2x^4 + 81 + 18x^2x4+81+18x2

Sắp xếp: x4+18x2+81x^4 + 18x^2 + 81x4+18x2+81
Dạng: (x2+9)2(x^2 + 9)^2(x2+9)2

6) 4x2−20x+254x^2 - 20x + 254x2−20x+25

Dạng: (2x−5)2(2x - 5)^2(2x−5)2

7) 8x3−12x2+6x−18x^3 - 12x^2 + 6x - 18x3−12x2+6x−1

Gom nhóm: (8x3−12x2)+(6x−1)(8x^3 - 12x^2) + (6x - 1)(8x3−12x2)+(6x−1)
Hoặc nhận dạng lập phương: (2x−1)3=8x3−12x2+6x−1(2x - 1)^3 = 8x^3 - 12x^2 + 6x - 1(2x−1)3=8x3−12x2+6x−1
→ (2x−1)3(2x - 1)^3(2x−1)3

8) x3+3x2y+3xy2+y3x^3 + 3x^2y + 3xy^2 + y^3x3+3x2y+3xy2+y3

Dạng: (x+y)3(x + y)^3(x+y)3

9) x3−6x2y+12xy2−8y3x^3 - 6x^2y + 12xy^2 - 8y^3x3−6x2y+12xy2−8y3

Bài 2 :

1) (x+1)(x2−x+1)(x+1)(x^2 - x + 1)(x+1)(x2−x+1)

Dạng: (a+b)(a2−ab+b2)=a3+b3(a+b)(a^2 - ab + b^2) = a^3 + b^3(a+b)(a2−ab+b2)=a3+b3
Ở đây a=x,b=1a = x, b = 1a=x,b=1
→ x3+13=x3+1x^3 + 1^3 = x^3 + 1x3+13=x3+1

2) (x−1)(x2+x+1)(x-1)(x^2 + x + 1)(x−1)(x2+x+1)

Dạng: (a−b)(a2+ab+b2)=a3−b3(a-b)(a^2 + ab + b^2) = a^3 - b^3(a−b)(a2+ab+b2)=a3−b3
a=x,b=1a = x, b = 1a=x,b=1
→ x3−13=x3−1x^3 - 1^3 = x^3 - 1x3−13=x3−1

3) (x−2)(x2+2x+4)(x-2)(x^2 + 2x + 4)(x−2)(x2+2x+4)

Dạng: (a−b)(a2+ab+b2)=a3−b3(a-b)(a^2 + ab + b^2) = a^3 - b^3(a−b)(a2+ab+b2)=a3−b3
a=x,b=2a = x, b = 2a=x,b=2
→ x3−23=x3−8x^3 - 2^3 = x^3 - 8x3−23=x3−8

4) (x+2)(x2−2x+4)(x+2)(x^2 - 2x + 4)(x+2)(x2−2x+4)

Dạng: (a+b)(a2−ab+b2)=a3+b3(a+b)(a^2 - ab + b^2) = a^3 + b^3(a+b)(a2−ab+b2)=a3+b3
a=x,b=2a = x, b = 2a=x,b=2
→ x3+23=x3+8x^3 + 2^3 = x^3 + 8x3+23=x3+8

5) (x−3)(x2+3x+9)(x-3)(x^2 + 3x + 9)(x−3)(x2+3x+9)

Dạng: (a−b)(a2+ab+b2)=a3−b3(a-b)(a^2 + ab + b^2) = a^3 - b^3(a−b)(a2+ab+b2)=a3−b3
a=x,b=3a = x, b = 3a=x,b=3
→ x3−27x^3 - 27x3−27

6) (x−4)(x2+4x+16)(x-4)(x^2 + 4x + 16)(x−4)(x2+4x+16)

Dạng: (a−b)(a2+ab+b2)=a3−b3(a-b)(a^2 + ab + b^2) = a^3 - b^3(a−b)(a2+ab+b2)=a3−b3
a=x,b=4a = x, b = 4a=x,b=4
→ x3−64x^3 - 64x3−64

7) (4x−3y)(16x2+9y2+12xy)(4x - 3y)(16x^2 + 9y^2 + 12xy)(4x−3y)(16x2+9y2+12xy)

Dạng: (a−b)(a2+ab+b2)=a3−b3(a-b)(a^2 + ab + b^2) = a^3 - b^3(a−b)(a2+ab+b2)=a3−b3
a=4x,b=3ya = 4x, b = 3ya=4x,b=3y
→ (4x)3−(3y)3=64x3−27y3(4x)^3 - (3y)^3 = 64x^3 - 27y^3(4x)3−(3y)3=64x3−27y3

8) (3x−4y)(9x2+16y2+12xy)(3x - 4y)(9x^2 + 16y^2 + 12xy)(3x−4y)(9x2+16y2+12xy)

Dạng: (a−b)(a2+ab+b2)=a3−b3(a-b)(a^2 + ab + b^2) = a^3 - b^3(a−b)(a2+ab+b2)=a3−b3
a=3x,b=4ya = 3x, b = 4ya=3x,b=4y
→ (3x)3−(4y)3=27x3−64y3(3x)^3 - (4y)^3 = 27x^3 - 64y^3(3x)3−(4y)3=27x3−64y3

Bài 3

1) (−x−2)3+(2x−4)(x2+2x+4)−x2(x−6)(-x - 2)^3 + (2x - 4)(x^2 + 2x + 4) - x^2(x - 6)(−x−2)3+(2x−4)(x2+2x+4)−x2(x−6)

(−x−2)3=(−(x+2))3=−(x+2)3=−(x3+6x2+12x+8)(-x - 2)^3 = (-(x+2))^3 = -(x+2)^3 = -(x^3 + 6x^2 + 12x + 8)(−x−2)3=(−(x+2))3=−(x+2)3=−(x3+6x2+12x+8)
→ −x3−6x2−12x−8-x^3 - 6x^2 - 12x - 8−x3−6x2−12x−8
(2x−4)(x2+2x+4)=2(x−2)(x2+2x+4)(2x - 4)(x^2 + 2x + 4) = 2(x - 2)(x^2 + 2x + 4)(2x−4)(x2+2x+4)=2(x−2)(x2+2x+4)
Dạng a−b,a2+ab+b2a - b, a^2 + ab + b^2a−b,a2+ab+b2 → x3−8x^3 - 8x3−8
→ 2(x3−8)=2x3−162(x^3 - 8) = 2x^3 - 162(x3−8)=2x3−16
−x2(x−6)=−x3+6x2-x^2(x - 6) = -x^3 + 6x^2−x2(x−6)=−x3+6x2

Cộng lại:

(−x3−6x2−12x−8)+(2x3−16)+(−x3+6x2)(-x^3 - 6x^2 - 12x - 8) + (2x^3 - 16) + (-x^3 + 6x^2)(−x3−6x2−12x−8)+(2x3−16)+(−x3+6x2)

→ (−x3+2x3−x3)=0(-x^3 + 2x^3 - x^3) = 0(−x3+2x3−x3)=0, (−6x2+6x2)=0(-6x^2 + 6x^2) = 0(−6x2+6x2)=0

→ Còn lại −12x−8−16=−12x−24-12x - 8 - 16 = -12x - 24−12x−8−16=−12x−24

Kết quả: −12x−24=−12(x+2)-12x - 24 = -12(x + 2)−12x−24=−12(x+2)

2) (x−1)3−(x+2)(x2−2x+4)+3(x+4)(x−4)(x - 1)^3 - (x + 2)(x^2 - 2x + 4) + 3(x + 4)(x - 4)(x−1)3−(x+2)(x2−2x+4)+3(x+4)(x−4)

(x−1)3=x3−3x2+3x−1(x - 1)^3 = x^3 - 3x^2 + 3x - 1(x−1)3=x3−3x2+3x−1
(x+2)(x2−2x+4)(x + 2)(x^2 - 2x + 4)(x+2)(x2−2x+4) dạng a+b,a2−ab+b2a+b, a^2 - ab + b^2a+b,a2−ab+b2 → x3+8x^3 + 8x3+8
→ Lấy dấu trừ: −x3−8-x^3 - 8−x3−8
3(x+4)(x−4)=3(x2−16)=3x2−483(x + 4)(x - 4) = 3(x^2 - 16) = 3x^2 - 483(x+4)(x−4)=3(x2−16)=3x2−48

Cộng lại:

x3−3x2+3x−1−x3−8+3x2−48x^3 - 3x^2 + 3x - 1 - x^3 - 8 + 3x^2 - 48x3−3x2+3x−1−x3−8+3x2−48

→ x3−x3=0x^3 - x^3 = 0x3−x3=0, −3x2+3x2=0-3x^2 + 3x^2 = 0−3x2+3x2=0

→ Còn lại 3x−1−8−48=3x−573x - 1 - 8 - 48 = 3x - 573x−1−8−48=3x−57

Kết quả: 3x−573x - 573x−57

3) (x+y)(x2−xy+y2)+3(2x−y)(4x2+2xy+y2)(x + y)(x^2 - xy + y^2) + 3(2x - y)(4x^2 + 2xy + y^2)(x+y)(x2−xy+y2)+3(2x−y)(4x2+2xy+y2)

(x+y)(x2−xy+y2)=x3+y3(x + y)(x^2 - xy + y^2) = x^3 + y^3(x+y)(x2−xy+y2)=x3+y3
(2x−y)(4x2+2xy+y2)(2x - y)(4x^2 + 2xy + y^2)(2x−y)(4x2+2xy+y2) dạng a−b,a2+ab+b2a - b, a^2 + ab + b^2a−b,a2+ab+b2 với a=2x,b=ya = 2x, b = ya=2x,b=y
→ (2x)3−y3=8x3−y3 (2x)^3 - y^3 = 8x^3 - y^3(2x)3−y3=8x3−y3
→ Nhân 3: 24x3−3y324x^3 - 3y^324x3−3y3

Cộng lại:

x3+y3+24x3−3y3=25x3−2y3x^3 + y^3 + 24x^3 - 3y^3 = 25x^3 - 2y^3x3+y3+24x3−3y3=25x3−2y3

Kết quả: 25x3−2y325x^3 - 2y^325x3−2y3

4) (x+3y)(x2−3xy+9y2)+(3x−y)(9x2+3xy+y2)(x + 3y)(x^2 - 3xy + 9y^2) + (3x - y)(9x^2 + 3xy + y^2)(x+3y)(x2−3xy+9y2)+(3x−y)(9x2+3xy+y2)

(x+3y)(x2−3xy+9y2)(x + 3y)(x^2 - 3xy + 9y^2)(x+3y)(x2−3xy+9y2) dạng a+b,a2−ab+b2a+b, a^2 - ab + b^2a+b,a2−ab+b2 với a=x,b=3ya = x, b = 3ya=x,b=3y
→ x3+27y3x^3 + 27y^3x3+27y3
(3x−y)(9x2+3xy+y2)(3x - y)(9x^2 + 3xy + y^2)(3x−y)(9x2+3xy+y2) dạng a−b,a2+ab+b2a-b, a^2 + ab + b^2a−b,a2+ab+b2 với a=3x,b=ya = 3x, b = ya=3x,b=y
→ 27x3−y327x^3 - y^327x3−y3

Cộng lại:

x3+27y3+27x3−y3=28x3+26y3x^3 + 27y^3 + 27x^3 - y^3 = 28x^3 + 26y^3x3+27y3+27x3−y3=28x3+26y3

Kết quả: 28x3+26y328x^3 + 26y^328x3+26y3

Bài 4

1) 8x3−12x2+6x−1=08x^3 - 12x^2 + 6x - 1 = 08x3−12x2+6x−1=0

Dạng (2x−1)3=0(2x - 1)^3 = 0(2x−1)3=0
→ 2x−1=0⇒x=122x - 1 = 0 \Rightarrow x = \frac122x−1=0⇒x=21

2) x3−6x2+12x−8=27x^3 - 6x^2 + 12x - 8 = 27x3−6x2+12x−8=27

Vế trái: (x−2)3=27(x - 2)^3 = 27(x−2)3=27
→ x−2=3⇒x=5x - 2 = 3 \Rightarrow x = 5x−2=3⇒x=5

3) x2−8x+16=5(4−x)3x^2 - 8x + 16 = 5(4 - x)^3x2−8x+16=5(4−x)3

Vế trái: (x−4)2(x - 4)^2(x−4)2
Vế phải: 5(−(x−4))3=−5(x−4)35(-(x - 4))^3 = -5(x - 4)^35(−(x−4))3=−5(x−4)3

Phương trình: (x−4)2=−5(x−4)3(x - 4)^2 = -5(x - 4)^3(x−4)2=−5(x−4)3

→ Đặt t=x−4t = x - 4t=x−4

→ t2=−5t3t^2 = -5t^3t2=−5t3

→ t2+5t3=0t^2 + 5t^3 = 0t2+5t3=0

→ t2(1+5t)=0t^2(1 + 5t) = 0t2(1+5t)=0

→ t=0t = 0t=0 hoặc t=−15t = -\frac15t=−51

→ x=4x = 4x=4 hoặc x=4−15=195x = 4 - \frac15 = \frac{19}{5}x=4−51=519

4) (2−x)3=6x(x−2)(2 - x)^3 = 6x(x - 2)(2−x)3=6x(x−2)

Nhận thấy 2−x=−(x−2)2 - x = -(x - 2)2−x=−(x−2)
→ Vế trái: (−(x−2))3=−(x−2)3(-(x - 2))^3 = -(x - 2)^3(−(x−2))3=−(x−2)3
Phương trình: −(x−2)3=6x(x−2)-(x - 2)^3 = 6x(x - 2)−(x−2)3=6x(x−2)

Nếu x−2=0⇒x=2x - 2 = 0 \Rightarrow x = 2x−2=0⇒x=2 (thỏa)

Nếu x≠2x e 2x=2: Chia cả hai vế cho x−2x - 2x−2

→ −(x−2)2=6x-(x - 2)^2 = 6x−(x−2)2=6x

→ −(x2−4x+4)=6x- (x^2 - 4x + 4) = 6x−(x2−4x+4)=6x

→ −x2+4x−4=6x-x^2 + 4x - 4 = 6x−x2+4x−4=6x

→ −x2−2x−4=0-x^2 - 2x - 4 = 0−x2−2x−4=0

→ x2+2x+4=0x^2 + 2x + 4 = 0x2+2x+4=0 (vô nghiệm thực)

Kết quả: x=2x = 2x=2

5) (x+1)3−(x−1)3−6(x−1)2=−10(x + 1)^3 - (x - 1)^3 - 6(x - 1)^2 = -10(x+1)3−(x−1)3−6(x−1)2=−10

(x+1)3−(x−1)3=[(x+1)−(x−1)][(x+1)2+(x+1)(x−1)+(x−1)2]=(2)[(x2+2x+1)+(x2−1)+(x2−2x+1)]=2[3x2+1]=6x2+2(x + 1)^3 - (x - 1)^3 = [ (x + 1) - (x - 1) ] [ (x + 1)^2 + (x + 1)(x - 1) + (x - 1)^2 ] = (2) [ (x^2 + 2x + 1) + (x^2 - 1) + (x^2 - 2x + 1) ] = 2[3x^2 + 1] = 6x^2 + 2(x+1)3−(x−1)3=[(x+1)−(x−1)][(x+1)2+(x+1)(x−1)+(x−1)2]=(2)[(x2+2x+1)+(x2−1)+(x2−2x+1)]=2[3x2+1]=6x2+2

Phương trình: 6x2+2−6(x2−2x+1)=−106x^2 + 2 - 6(x^2 - 2x + 1) = -106x2+2−6(x2−2x+1)=−10

→ 6x2+2−6x2+12x−6=−106x^2 + 2 - 6x^2 + 12x - 6 = -106x2+2−6x2+12x−6=−10

→ 12x−4=−1012x - 4 = -1012x−4=−10

→ 12x=−612x = -612x=−6

→ x=−12x = -\frac12x=−21

6) (3−x)3−(x+3)3=36x2−54x(3 - x)^3 - (x + 3)^3 = 36x^2 - 54x(3−x)3−(x+3)3=36x2−54x

Vế trái: Dùng hằng đẳng thức a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a-b)(a^2 + ab + b^2)a3−b3=(a−b)(a2+ab+b2)
a=3−x,b=x+3a = 3 - x, b = x + 3a=3−x,b=x+3
a−b=(3−x)−(x+3)=−2xa - b = (3 - x) - (x + 3) = -2xa−b=(3−x)−(x+3)=−2x
a2+ab+b2=(x2−6x+9)+[(3−x)(x+3)]+(x2+6x+9)a^2 + ab + b^2 = (x^2 - 6x + 9) + [(3 - x)(x + 3)] + (x^2 + 6x + 9)a2+ab+b2=(x2−6x+9)+[(3−x)(x+3)]+(x2+6x+9)
= x2−6x+9+(9−x2)+x2+6x+9=x2+18x^2 - 6x + 9 + (9 - x^2) + x^2 + 6x + 9 = x^2 + 18x2−6x+9+(9−x2)+x2+6x+9=x2+18

→ Vế trái = (−2x)(x2+18)=−2x3−36x(-2x)(x^2 + 18) = -2x^3 - 36x(−2x)(x2+18)=−2x3−36x

Phương trình: −2x3−36x=36x2−54x-2x^3 - 36x = 36x^2 - 54x−2x3−36x=36x2−54x

→ −2x3−36x−36x2+54x=0-2x^3 - 36x - 36x^2 + 54x = 0−2x3−36x−36x2+54x=0

→ −2x3−36x2+18x=0-2x^3 - 36x^2 + 18x = 0−2x3−36x2+18x=0

→ −2x(x2+18x−9)=0-2x(x^2 + 18x - 9) = 0−2x(x2+18x−9)=0

→ x=0x = 0x=0 hoặc x2+18x−9=0x^2 + 18x - 9 = 0x2+18x−9=0

→ x=−9±81+9=−9±90=−9±310x = -9 \pm \sqrt{81 + 9} = -9 \pm \sqrt{90} = -9 \pm 3\sqrt{10}x=−9±81+9

=−9±90

=−9±310

Kết quả: x=0x = 0x=0 hoặc x=−9±310x = -9 \pm 3\sqrt{10}x=−9±310