chịu

\(\dfrac{a\sqrt{a}+b\sqrt{b}}{2\sqrt{a}+2\sqrt{b}}=\dfrac{a-\sqrt{ab}+b}{2}\)

\(=\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}{2\left(\sqrt{a}+\sqrt{b}\right)}=\dfrac{a+\sqrt{ab}+b}{2}\)

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

=(a−1−b+1)(a−1+b−1)=(a−b)(a+b−2) 

hằng đẳng thức số 3

đây là một hằng đẳng thức nha bạn

=a³+b³+c³-3abc

thank

cho mình cách giải

`Answer:`

`a)`

`A=5(x+1)^2-3(x-3)^2-4(x^2-4)`

`=>A=5(x^2+2x+1)-3(x^2-6x+9)-4x^2+16`

`=>A=5x^2+10x+5-3x^2+18x-27-4x^2+16`

`=>A=(5x^2-3x^2-4x^2)+(10x+18x)+(5-27+16)`

`=>A=-2x^2+28x-6`

`b)`

`B=5(x+1)^2-3(x-3)^2-4(x+2)(x-2)`

`=2x(3x+5)-3(3x+5)-2x(x^2-4x+4)-[(2x)^2-3^2]`

`=6x^2+10x-9x-15-2x^3+8x^2-8x-4x^2+9`

`=(6x^2-4x^2+8x^2)-2x^3+(10x-9x-8x)+(-15+9)`

Thay `x=-7` vào ta được:

`B=10(-7)^2-2(-7)^3-7(-7)-6`

`=>B=10.49-2(-343)+49-6`

`=>B=490+686+49-6`

`=>B=1219`

a) \(A=1+3+3^2+...+3^{100}\)

\(3A=3+3^2+3^3+...+3^{101}\)

\(3A-A=\left(3+3^2+3^3+...+3^{101}\right)-\left(1+3+3^2+...+3^{100}\right)\)

\(2A=3^{101}-1\)

\(A=\frac{3^{101}-1}{2}\)

b) \(B=2^{100}-2^{99}+2^{98}-2^{97}+...-2^3+2^2-2+1\)

\(2B=2^{101}-2^{100}+2^{99}-2^{98}+...-2^4+2^3-2^2+2\)

\(B+2B=\left(2^{100}-2^{99}+...-2+1\right)+\left(2^{101}-2^{100}+...-2^2+2\right)\)

\(3B=2^{101}+1\)

\(B=\frac{2^{101}+1}{3}\)

(a + b + c) . (a + b + c) - 2.(a . b + b . c + c . a)

= a . a + a . b + a . c + b . a + b . b + b . c + c . a + c . b + c . c - 2ab - 2bc - 2ca

= a² + ab + ac + ab + b² + bc + ac + bc + c² - 2ab - 2bc - 2ca

= a² + b² + (ab + ab) + (bc + bc) + (ac + ac) - 2ab - 2bc - 2ca

= a² + b² + 2ab + 2bc + 2ca - 2ab - 2bc - 2ca

= a² + b². 

\(A=\sqrt{64a^2}\cdot2a=\sqrt{\left(8a\right)^2}\cdot2a=\left|8a\right|\cdot2a\)

Với a < 0 A = 8a.(-2a) = -16a²

Với a ≥ 0 A = 8a.2a = 16a²

\(B=3\sqrt{9a^6}-6a^3=3\sqrt{\left(3a^3\right)^2}-6a^3=9\left|a^3\right|-6a^3\)