(-a-b)²=[-1(a+b)]²=(-1)²(a+b)²=(a+b)² (đpcm)

(–a – b)2 = [(– 1).(a + b)]2

 = (–1)2(a + b)2

 = 1.(a + b)2

 = (a + b)2 (đpcm)

thêm x²+y²+z²=1 nha

thêm x² + y² + z² = 1 nha

      HT nha vinh

\(ab+bc+ca\ge3\sqrt[3]{a^2b^2c^2}=3\sqrt[3]{9}\)

Dấu \(=\)khi \(a=b=c=\sqrt[3]{3}\).

chịu bó tay

??????

Trả lời:

Bài 1:

a, \(-2x\left(x-3\right)=-2x^2+6x\)

b, \(-4xy\left(x-3xy^2\right)=-4x^2y+12x^2y^3\)

d, \(\left(x-3\right)\left(x-4\right)=x^2-4x-3x+12=x^2-7x+12\)

e, \(\left(x-y\right)\left(x+y\right)=x^2-y^2\)

Bài 2: 

a, \(2\left(x-1\right)-3\left(2x-2\right)=2x-2-6x+6=-4x+4\)

b, \(x\left(x-y\right)-y\left(y-x\right)=x^2-xy-y^2+xy=x^2-y^2\)

c, \(3x\left(x+1\right)-2x\left(x-3\right)=3x^2+3x-2x^2+6x=x^2+9x\)

d, \(-4x\left(x-1\right)+\left(2x+1\right)\left(2x+5\right)=-4x^2+4x+4x^2+10x+2x+5=16x+5\)

e, \(\left(x-2\right)\left(x-3\right)-\left(x-1\right)\left(x-4\right)=x^2-5x+6-x^2+5x-4=2\)

f, \(\left(x-4\right)^2=x^2-8x+16\)

Bài 3:

a, \(4\left(x+3\right)-5\left(x-1\right)=-7\)

\(\Leftrightarrow4x+12-5x+5=-7\)

\(\Leftrightarrow17-x=-7\)

\(\Leftrightarrow-x=-24\)

\(\Leftrightarrow x=24\)

Vậy x = 24 là nghiệm của pt.

b, \(x\left(x-5\right)-\left(x+2\right)x=9\)

\(\Leftrightarrow x^2-5x-x^2-2x=9\)

\(\Leftrightarrow-7x=9\)

\(\Leftrightarrow x=-\frac{9}{7}\)

Vậy x = - 9/7 là nghiệm của pt.

a) 4x² + 4xy + y² 

= (2x + y)²

b) (2x + 1)² - (x - 1)² 

= (2x + 1  + x - 1)(2x + 1 - x + 1)

= 3x(x + 2) 

c) 9 - 6x + x² - y² 

 = (x² - 6x + 9) - y² 

= (x - 3)² - y² 

 = (x - y - 3)(x + y - 3) 

d) (-x - 2) + 3(x² - 4) 

 = -(x + 2) + 3(x - 2)(x + 2) 

 = (x + 2)(3x - 7) 

e) 5x²- 10xy² + 5y⁴

= 5(x² - 2xy² + y⁴) 

 = 5(x - y²)² 

f) \(\frac{x^4}{2}-2x^2=\frac{x^4-4x^2}{2}=\frac{x^2\left(x^2-4\right)}{2}=\frac{x^2\left(x-2\right)\left(x+2\right)}{2}\)

g) 49(x - 4)² - 9(x + 2)² 

 = (7x - 28)² - (3x + 6)² 

 = (10x - 22)(4x - 34) 

h) (x² + y² - 5)² - 2(xy + 2)²

= \(\left(x^2+y^2-5\right)^2-\left(\sqrt{2}xy+2\sqrt{2}\right)^2\)

\(=\left(x^2+y^2+2\sqrt{xy}+2\sqrt{2}-5\right)\left(x^2+y^2-\sqrt{2}xy-2\sqrt{2}-5\right)\)

a, \(\left(y-2\right)\left(y+2\right)\left(y^2+4\right)-\left(y+3\right)\left(y-3\right)\left(y^2+9\right)\)

\(=\left(y^2-4\right)\left(y^2+4\right)-\left(y^2-9\right)\left(y^2+9\right)\)

\(=y^4-16-y^4+81=65\)

b, \(2\left(x^2-xy+y^2\right)\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)-2\left(x^6-y^6\right)\)

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

\(=2\left(x^6-y^6\right)-2\left(x^6-y^6\right)=0\)