\(a\left(b+1\right)+b\left(a+1\right)=\left(a+1\right)\left(b+1\right)\)

\(\Leftrightarrow ab+a+ab+b=ab+a+b+1\Leftrightarrow ab=1\left(dpcm\right)\)

mệnh đề đúng , đó là truong hop = nhau cua 2 tg (g.c.g) bn xem cách cm ở trg sách gk

gọi v la vân toc oto di tu A đến B ta có pt

3v + 3.2v/3 = 150

v = 30km/h

AB = 150/30 =5h

BA = 150: (2.30:3) = 7h30p

Xét \(VP=4p.\left(p-a\right)=2p.2.\left(p-a\right)=2p.\left(2p-2a\right)=\left(a+b+c\right)\left(b+c-a\right)\)

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

Vậy ta có đpcm

2bc+b^2+c^2-a^2=(b+c)^2-a^2=(b+c-a)(b+c+a)=(2p-a-a)2p=(2p-2a)2p=2.2p(p-a)=4p(p-a)

(3x-5)(7-5x)-(5x+2)(2-3x)=4

21x - 35 - 15x^2 + 25x - (10x +4 - 15x^2 -6x) =4

46x - 10x +6x = 4 + 35 +4

42x = 43

x= 43/42

\(\left(3x-5\right)\left(7-5x\right)-\left(5x+2\right)\left(2-3x\right)=4\)

\(3x.\left(7-5x\right)-5.\left(7-5x\right)-5x.\left(2-3x\right)+2.\left(2-3x\right)=4\)

\(3x.7-3x.5x-5.7+5.5x-5x.2+5x.3x+2.2-2.3x=4\)

\(21x-15x^2-35+25x-10x+15x^2+4-6x=4\)

\(30x-31=4\)

\(\Rightarrow30x=4+31\)

\(\Rightarrow30x=35\)

\(\Rightarrow x=35\div30\)

\(\Rightarrow x=\frac{7}{6}\)

1) \(x^3-x+y^3-y\)

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

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

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

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

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

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

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

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

2.\(3\left(x^2+6xy+y^2-z^2\right)=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y+z\right)\left(x+y-z\right)\)

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

cho mình nha