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