Question
Factorize of the following expressions: $x^3-2 x^2 y+3 x y^2-6 y^3 $
✓
Answer
$x^3-2 x^2 y+3 x y^2-6 y^3 $
$ =\left(x^3-2 x^2 y\right)+\left(3 x y^2-6 y^3\right) $
$ =x^2(x-2 y)+3 y^2(x-2 y) $
$ =\left(x^2+3 y^2\right)(x-2 y) [$taking $(x - 2y)$ as the common factor$]$
$ =\left(x^3-2 x^2 y\right)+\left(3 x y^2-6 y^3\right) $
$ =x^2(x-2 y)+3 y^2(x-2 y) $
$ =\left(x^2+3 y^2\right)(x-2 y) [$taking $(x - 2y)$ as the common factor$]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the area of polygon $M N O P Q R$, If $M P=9 cm$, $M D=7 cm, M C=6 cm$, $M B=4 cm, M A=2 cm . N A O C$, $Q D$ and $R B$ are perpendiculars to diagonal MP.
→The shape of the top surface of a table is a trapezium. Find its area, if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m .
Write the value of $(13)^{-13}+(13)^{13}$.
→Simplify:$\frac{16\text{m}^3\text{y}^2}{4\text{m}^2\text{y}}$
→A milk container is $8\ cm$ long and $50\ cm$ wide. What should be its height so that it can hold $4$ litres of milk$?$
→Write the greatest common factor in each of the following terms.
$-18a^2, 108a$
→$-18a^2, 108a$
Find the square root of number by using the method of prime factorisation: $8100$
→Find the square root of number by using the method of prime factorisation: $11025$
→Solve:
$ a^4-(2 b+c)^4 $
→$ a^4-(2 b+c)^4 $
Using the given pattern, find the missing numbers:
$1^2+2^2+2^2=3^2 $
$ 2^2+3^2+6^2=7^2$
$ 3^2+4^2+12^2=13^2 $
$4^2+ 5^2+\_^2= 21^2$
$5^2+\_^2+ 30^2 = 31^2$
$6^2+ 7^2+\_\_\_^2=\_\_\_^2$
→$1^2+2^2+2^2=3^2 $
$ 2^2+3^2+6^2=7^2$
$ 3^2+4^2+12^2=13^2 $
$4^2+ 5^2+\_^2= 21^2$
$5^2+\_^2+ 30^2 = 31^2$
$6^2+ 7^2+\_\_\_^2=\_\_\_^2$