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Factorisation by Regrouping Terms

Factorise: x3...

Question

Factorise:

$x^{3} - 2 x^{2} y + 3 x y^{2} - 6 y^{3}$

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Solution

$x^{3} - 2 x^{2} y + 3 x y^{2} - 6 y^{3} = x^{2} (x - 2 y) + 3 y^{2} (x - 2 y) = (x - 2 y) (x^{2} + 3 y^{2})$

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Similar questions

Q. Factorize each of the following expressions:
x³ − 2x²y + 3xy² − 6y³

{2 x}^{2} y - {3 x y}^{2} + {2 x}^{2} y - {4 x}^{2} y + {2 x y}^{2}

- 2 x^{2} y + 3 x y^{2}

8 x^{2} y

Q. State True or False:
On subtracting

- 2 x^{2} y + 3 x y^{2}

8 x^{2} y

, the answer is

10 x^{2} y - 3 x y^{2}

.

Q. What is the remainder when

3 x^{3} - 2 x^{2} y - 3 x y^{2} - 10 y^{3}

x - 2 y

?

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