Question
Factorize the following expressions:
$54 x^6 y+2 x^3 y^4$
$54 x^6 y+2 x^3 y^4$
✓
Answer
$54 x^6 y+2 x^3 y^4$
$=2 x^3 y\left(27 x^3+y^3\right)$
$=2 x^3 y\left((3 x)^3+y^3\right)$
$=2 x^3 y(3 x+y)\left((3 x)^2-3 x \times y+y^2\right)$
$\therefore\left[a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$=2 x^3 y(3 x+y)\left(9 x^2-3 x y+y^2\right)$
$\therefore 54 x^6 y+2 x^3 y^4=2 x^3 y(3 x+y)\left(9 x^2-3 x y+y^2\right)$
$=2 x^3 y\left(27 x^3+y^3\right)$
$=2 x^3 y\left((3 x)^3+y^3\right)$
$=2 x^3 y(3 x+y)\left((3 x)^2-3 x \times y+y^2\right)$
$\therefore\left[a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$=2 x^3 y(3 x+y)\left(9 x^2-3 x y+y^2\right)$
$\therefore 54 x^6 y+2 x^3 y^4=2 x^3 y(3 x+y)\left(9 x^2-3 x y+y^2\right)$
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