How do you multiply $(2 x^{2} + y^{2}) (x - 2 y)$ $(2x^2 + y^2)(x - 2y)$ ?

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Answer 1 · 2015-06-26T13:50:46

$= 2 x^{3} - 4 x^{2} y + x y^{2} - 2 y^{3}$ $= color(blue)(2x^3 - 4x^2y + xy^2 -2y^3)$

$(2 x^{2} + y^{2}) . (x - 2 y)$ $color(blue)( (2x^2+y^2)) . (x−2y)$

$= (2 x^{2}) . (x) + 2 x^{2} . (- 2 y)$ $=color(blue)( (2x^2)) . (x) + color(blue)(2x^2) . (−2y)$

$= 2 x^{3} - 4 x^{2} y$ $=color(blue)( 2x^3 color(blue)(-4x^2y)$ .............. $(1)$ $(1)$

Multiplying $y^{2}$ $color(blue)(y^2)$ with both terms of the second bracket
$= (y^{2}) . (x) + y^{2} . (- 2 y)$ $=color(blue)( (y^2)) . (x) + color(blue)(y^2) . (−2y)$

$= x y^{2} - 2 y^{3}$ $=color(blue)( xy^2 - 2y^3$ ............. $(2)$ $(2)$

Combining $1$ $1$ and $2$ $2$
$= 2 x^{3} - 4 x^{2} y + x y^{2} - 2 y^{3}$ $= color(blue)(2x^3 - 4x^2y + xy^2 -2y^3)$

How do you multiply (2x^2 + y^2)(x - 2y) (2x2+y2)(x−2y) (2x^2 + y^2)(x - 2y) ?