If one of the two factors of an expression which is the difference of two cubes is ( $x^{4}$ + $x^{2}$ y + $y^{2}$ ), then the other factor would be -

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Solution

$x^{4}$ + $x^{2}$ y + $y^{2}$ = ${(x^{2})}^{2}$ + $x^{2}$ y + ${(y)}^{2}$

This is in the form of $a^{2}$ + ab + $b^{2}$ where a = $x^{2}$ , b = y

The other factor is a – b as $a^{3}$ – $b^{3}$ = (a - b)( $a^{2}$ + ab + $b^{2}$ )

Hence, other factor of $x^{4}$ + $x^{2}$ y + $y^{2}$ is $x^{2}$ - y

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If one of the two factors of an expression which is the difference of two cubes is (x4 + x2y + y2), then the other factor would be -

x4 + x2y + y2 = (x2)2 + x2y + (y)2 This is in the form of a2+ ab + b2 where a = x2, b = y The other factor is a – b as a3 – b3 = (a - b)( a2+ ab + b2) Hence, other factor of x4 + x2y + y2 is x2 - y

If one of the two factors of an expression which is the difference of two cubes is ( $x^{4}$ + $x^{2}$ y + $y^{2}$ ), then the other factor would be -