a(x+a)^2 4x^2 a(x^2+a^2+2ax) 4x^2 ax^2+a^3+2a^2x 4x^2 x^2(a 4)+x(2a^2)+a^3 (a 4)x^2+2a^2x+a^3=0 x= 2a^2±√((2a^2)^2 4(a 4)a^3)2(a 4 ...

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Binomial Expression

Factories a...

Question

Factories $a (x + a)^{2} - 4 x^{2}$ .

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Solution

$a (x + a)^{2} - 4 x^{2}$

$a (x^{2} + a^{2} + 2 a x) - 4 x^{2}$

$a x^{2} + a^{3} + 2 a^{2} x - 4 x^{2}$

$x^{2} (a - 4) + x (2 a^{2}) + a^{3}$

$(a - 4) x^{2} + 2 a^{2} x + a^{3} = 0$

$x = \frac{- 2 a^{2} \pm \sqrt{{(2 a^{2})}^{2} - 4 (a - 4) a^{3}}}{2 (a - 4)}$

$x = \frac{- a^{2} + 2 a^{\frac{3}{2}}}{a - 4}, - \frac{a^{2} + 2 a^{\frac{3}{2}}}{a - 4}$

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