Factorise the following by taking out the common factors:12a^3+ 1… - Vidyadip

Question

Factorise the following by taking out the common factors:$12a^3+ 15a^2b - 21ab^2$

✓

Answer

$12 a^3+15 a^2 b-21 a b^2$
Here, the common factor is $3 a$.
Dividing throughout by $3 a$, we get
$\frac{12 a^3}{3 a}+\frac{15 a^2 b}{3 a}-\frac{21 a b^2}{3 a} $
$=4 a^2+5 a b-7 b^2 $
$\therefore 12 a^3+15 a^2 b-21 a b^2 $
$=3 a\left(4 a^2+5 a b-7 b^2\right) .$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[3 marks sum]" from Factorisation→Factorisation — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

Construct a frequency table from the following data :

Age (in years)	Number of students
Less than 10	6
Less than 20	14
Less than 30	30
Less than 40	52
Less than 50	65
Less than 60	70

Two parallel chords AB and CD are 3.9 cm apart and lie on the opposite sides of the centre of a circle. If AB = 1.4 cm and CD = 4 cm, find the radius of the circle.

Show that the product of a non$-$zero rational number and an irrational number is an irrational number.

Solve for $x:\sqrt{\left(8^0+\frac{2}{3}\right)}=(0.6)^{2-3 x}$

Factorise : $50 a^2-2(b-c)^2$

How many liters of water will flow out of a pipe having a cross sectional area $6 \ cm^2$ in one hour, if the speed of water in the pipe is $30 \ cm/sec$?

Find the area of a triangle with a base $12 \ cm$ and a height equal to the width of a rectangle having area of $96 \ cm^2$ and a length of $12 \ cm.$

Solve the equation:
$\frac{3}{2 x}+\frac{2}{3 y}=5, \frac{5}{x}-\frac{3}{y}=1$

The sum of four times the first number and three times the second number is $15.$ The difference of three times the first number and twice the second number is $7.$ Find the numbers.

A model of cargo tuck is made to a scale of $1:40.$ The length of the model is $15\ cm.$ Calculate: The volume of the model if the volume of the truck is $6\ m^3$