b: Ta có: \(\left(4x-y\right)\left(4x+y\right)-2\left(3x-2y\right)^2+\left(x-3y\right)^2\)

\(=16x^2-y^2-2\left(9x^2-12xy+4y^2\right)+x^2-6xy+9y^2\)

\(=17x^2-6xy+8y^2-18x^2+24xy-8y^2\)

\(=-x^2+18xy\)

c: Ta có: \(\left(2a-3b+4c\right)\left(2a-3b-4c\right)\)

\(=\left(2a-3b\right)^2-16c^2\)

\(=4a^2-12ab+9b^2-16c^2\)

a) \(\left(x^2-2x+2\right)\left(x-2\right)\left(x^2-2x+2\right)\left(x+2\right)\)

\(=\left(x^3-2x^2-2x^2+4x+2x-4\right)\left(x^3+2^3\right)\)

\(=\left(x^3-4x^2+6x-4\right)\left(x^3+8\right)\)

\(=x^6+8x^3-4x^5-32x^2+6x^4+48x-4x^3-32\)

\(=x^6-4x^5+4x^3-32x^2+48x-32\)

b) \(\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)

\(=\left(x+1+x-1\right)\left[\left(x+1\right)^2-\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\right]+x^3-3x\left(x^2-1\right)\)

\(=2x\left[\left(x^2+2x+1\right)-\left(x^2-1\right)+\left(x^2-2x+1\right)\right]+x^3-\left(3x^3-3x\right)\)

\(=2x\left(x^2+2x+1-x^2+1+x^2-2x+1\right)+x^3-3x^3+3x\)

\(=2x\left(x^2+3\right)+x^3-3x^3+3x\)

\(=2x^3+6x-2x^3+3x\)

\(=9x\)

2 câu kia đợi tí đã nhé!

c) \(\left(a+b+c\right)^2+\left(a+b-c\right)^2+\left(2a-b\right)^2\)

\(=\left(a^2+b^2+c^2+2ab+2bc+2ca\right)+\left(a^2+b^2+c^2+2ab-2bc-2ca\right)+\left(4a^2-4ab+b^2\right)\)

\(=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2+2ab-2bc-2ca+4a^2-4ab+b^2\)

\(=6a^2+3b^2+2c^2\)

d) \(\left(a+b+c\right)^2+\left(a+b-c\right)^2+2\left(a+b\right)^2\)

\(=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2+2ab-2bc-2ca+2a^2+2ab+b^2\)

\(=4a^2+4b^2+2c^2+6ab.\)

a, \(\left(x^2-2x+2\right)\left(x-2\right)\left(x^2-2x+2\right)\left(x+2\right)\)

\(=\left(x^2-2x+2\right)^2.\left(x^2-4\right)\)

\(=\left(x^2+4x^2+4-4x^3+4x^2-8x\right)\left(x^2-4\right)\)

\(=\left(-4x^3+9x^2-8x+4\right)\left(x^2-4\right)\)

\(=-4x^5+16x^3+9x^4-36x^2-8x^3+32x+4x^2-16\)

\(=-4x^5+9x^4+8x^3-32x^2+32x-16\)

b, \(\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)

\(=x^3+3x^2+3x+1+x^3-3x^2+3x-1-3x\left(x^2-1\right)\)

\(=2x^3+6x-3x^3+3x=-x^3+9x\)

a. \(8x\left(x-2017\right)-2x+4034=0\)

\(8x\left(x-2017\right)-2\left(x-2017\right)=0\)

\(\left(8x-2\right)\left(x-2017\right)=0\)

\(\Rightarrow TH1:8x-2=0\)

\(8x=2\)

\(x=\frac{1}{4}\)

\(TH2:x-2017=0\)

\(x=2017\)

Vậy \(x\in\left\{\frac{1}{4};2017\right\}\)

Bài 1 

a) \(8x\left(x-2017\right)-2x+4034=0\)

\(\Rightarrow8x\left(x-2017\right)-2\left(x-2017\right)=0\)

\(\Rightarrow\left(x-2017\right)\left(4x-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=2017\\x=\frac{1}{4}\end{cases}}\)

B5:

a. \(\left(2-xy^2\right)^2-\left(2+xy^2\right)^2\)

\(=\left(2-xy+2+xy\right)\left(2-xy-2-xy\right)\)

\(=4xy\)

Đặt S=x+y, P=x.y
Ta có:S=2a-1, x^2+y^2=S^2-2P=a^2+2a-3
\Rightarrow P=\frac{1}{2}[(2a-1)^2-(a^2+2a-3)]=\frac{1}{2}(3a^2-6a+4)
Trước hết tìm a để hệ có nghiệm.
Điều kiện để hệ có nghiệm:S^2-4P \geq 0 \Leftrightarrow (2a-1)^2-2(3a^2-6a+4)\geq 0
\Leftrightarrow -2a^2+8a-7 \geq 0 \leftrightarrow 2-\frac{\sqrt{2}}{2} \leq a \leq 2+\frac{\sqrt{2}}{2}      (1)
Tìm a để P=\frac{1}{2}(3a^2-6a+4) đạt giá trị nhỏ nhất trên đoạn
        [2-\frac{\sqrt{2}}{2} ;2+\frac{\sqrt{2}}{2}]
Ta có hoành độ đỉnh a_0=\frac{6}{2.3}=1Parabol có bề lõm quay lên do đó \min P=P(2-\frac{\sqrt{2}}{2} )$
Vậy với a=2-\frac{\sqrt{2}}{2}  thì xy đạt giá trị nhỏ nhất.

Bài giải:

a) (a + b)² – (a – b)² = (a² + 2ab + b²) – (a² – 2ab + b²)

= a² + 2ab + b² – a² + 2ab - b² = 4ab

Hoặc (a + b)² – (a – b)² = [(a + b) + (a – b)][(a + b) – (a – b)]

= (a + b + a – b)(a + b – a + b)

= 2a . 2b = 4ab

b) (a + b)³ – (a – b)³ – 2b³

= (a³ + 3a²b + 3ab² + b³) – (a³ – 3a²b + 3ab² – b³) – 2b³

= a³ + 3a²b + 3ab² + b³ – a³ + 3a²b - 3ab² + b³ – 2b³

= 6a²b

Hoặc (a + b)³ – (a – b)³ – 2b³ = [(a + b)³ – (a – b)³] – 2b³

= [(a + b) – (a – b)][(a + b)² + (a + b)(a – b) + (a – b)²] – 2b³

= (a + b – a + b)(a² + 2ab + b² + a² – b² + a² – 2ab + b²) – 2b³

= 2b . (3a² + b²) – 2b³ = 6a²b + 2b³ – 2b³ = 6a²b

c) (x + y + z)² – 2(x + y + z)(x + y) + (x + y)²

= x² + y² + z²+ 2xy + 2yz + 2xz – 2(x² + xy + yx + y² + zx + zy) + x² + 2xy + y²

= 2x² + 2y² + z² + 4xy + 2yz + 2xz – 2x² – 4xy – 2y² – 2xz – 2yz = z²

a) \(\left(x+y\right)^2-\left(x-y\right)^2=x^2+2xy+y^2-x^2+2xy-y^2=4xy\)

b) \(\left(a+b\right)^3+\left(a-b\right)^3-2a^3=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3-2a^3\\ =6ab^2\)

c) \(9^8\times2^8-\left(18^4-1\right)\left(18^4+1\right)=18^8-18^8+1=1\)

a) \(A=\left(a-2b+c\right)-\left(a-2b-c\right)\)

\(A=a-2b+c-a+2b+c=2c\)

b) \(B=\left(-x-y+3\right)-\left(-x+2-y\right)\)

\(B=-x-y+3+x-2+y=1\)

c) \(C=2\left(3a+b-1\right)-3\left(2a+b-2\right)\)

\(C=6a+2b-2-6a-3b+6=4-b\)

a. \(A=\left(a-2b+c\right)-\left(a-2b-c\right)=a-2b+c-a+2b+c=0\) 

b. \(B=\left(-x-y+3\right)-\left(-x+2-y\right)=-x-y+3+x-2+y=1\)

c. \(C=2\left(3a+b-1\right)-3\left(2a+b-2\right)=6a+2b-2-6b-3b+6=4-3b\)

C = 4 - b nha@@