simplify-a-2-b-b-3-2ab-2-a-2-b-4b-3-4ab-3-

Question Number 172513 by Mikenice last updated on 28/Jun/22

s i m p l i f y

\sqrt{a^{2} b + b^{3} + 2 {a b}^{2}} - \sqrt{a^{2} b + 4 b^{3} + 4 {a b}^{3}}

Commented by Rasheed.Sindhi last updated on 28/Jun/22

D o y o u m e a n :

\sqrt{a^{2} b + b^{3} + 2 {a b}^{2}} - \sqrt{a^{2} b + 4 b^{3} + 4 {a b}^{2}}

Commented by Mikenice last updated on 28/Jun/22

y e s

Answered by Rasheed.Sindhi last updated on 28/Jun/22

\sqrt{a^{2} b + b^{3} + 2 {a b}^{2}} - \sqrt{a^{2} b + 4 b^{3} + 4 {a b}^{2}}

= \sqrt{b (a^{2} + b^{2} + 2 a b)} - \sqrt{b (a^{2} + 4 b^{2} + 4 a b)}

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

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

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

= - b \sqrt{b}

Answered by MJS_new last updated on 28/Jun/22

\sqrt{a^{2} b + b^{3} + 2 {a b}^{2}} =∣ a + b ∣ \sqrt{b}

\sqrt{a^{2} b + 4 b^{3} + 4 {a b}^{2}} =∣ a + 2 b ∣ \sqrt{b}

different results depending on a + b and

a + 2 b >=< 0

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