We use the above identity: ( a+b ) #160;^ 3 = a ^ 3 +3 a ^ 2 b+3a b ^ 2 + b ^ 3 . Take a=2x and b=3y and we get ( 2x+3y ) #160;^ 3 = ...

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Polynomial and Its General Form

Expand 2x+3...

Question

Expand ${(2 x + 3 y)}^{3}$ .

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Solution

As we know that the identity:
${(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$ .
Take $a = 2 x$ and $b = 3 y$ and we get
${(2 x + 3 y)}^{3} = {(2 x)}^{3} + 3 {(2 x)}^{2} (3 y) + 3 (2 x) {(3 y)}^{2} + {(3 y)}^{3}$
$= 8 x^{3} + 12 x^{2} (3 y) + 6 x (9 y^{2}) + 27 y^{3}$
$= 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}$
Hence, $(2 x + 3 y)^{3} = 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}$

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