Question

simplify (a+b)³-(a-b)³-6b(a²-b²)

Plz i need it fast

Answer 1

Answer:

[math](a^2 + b^2)^3 = a^6 + b^6 + 3a^4b^2 + 3a^2b^4[/math]

[math](a^3+b^3)^2 = a^6 + b^6 + 2a^3b^3[/math]

Given: [math](a^2 +b^2)^3 = (a^3+b^3)^2[/math]

[math]=> a^6 + b^6 + 3a^4b^2 + 3a^2b^4 = a^6 + b^6 + 2a^3b^3[/math]

[math]=> 3a^4b^2 + 3a^2b^4 = 2a^3b^3[/math]

[math]\div[/math] by [math]a^3b^3[/math] throughout

[math]=> \dfrac{3a}{b} + \dfrac{3b}{a} = 2[/math]

Let [math]\dfrac{a}{b} = x[/math]

[math]=> 3x + \dfrac{3}{x} = 2[/math]

[math]=> 3x^2 - 2x + 3 = 0[/math]

[math]=> x = \dfrac{2 \pm \sqrt{2^2 - (4*3*3)}}{2*3} = \dfrac{2 \pm \sqrt{-32}}{6}[/math]

[math]=> x = \dfrac{a}{b} = \dfrac{2 \pm 4\sqrt{2} i}{6} [/math]

[math]= \dfrac{1 \pm 2\sqrt{2}i}{3}[/math]