Question
Factorize:
$10m^3n^2+ 15m^4n - 20m^2n^3$
$10m^3n^2+ 15m^4n - 20m^2n^3$
✓
Answer
The greatest common factor of the terms
$10 m^3 n^2, 15 m^4 n$ and $-20 m^2 n^3$ of the expression $10 m^3 n^2+15 m^4 n-20 m^2 n^3$ is $5 m^2 n$
Now,
$ 10 m^3 n^2=5 m^2 n \cdot 2 m n $
$ 15 m^4 n=5 m^2 n \cdot 3 m^2 $
$ -20 m^2 n^3=5 m^2 n \cdot-4 n^2$
Hence, $10 m^3 n^2+15 m^2 n-20 m^2 n^3$ can be factorised as $5 m^2 n\left(2 m n+3 m^2-4 n^2\right)$.
$10 m^3 n^2, 15 m^4 n$ and $-20 m^2 n^3$ of the expression $10 m^3 n^2+15 m^4 n-20 m^2 n^3$ is $5 m^2 n$
Now,
$ 10 m^3 n^2=5 m^2 n \cdot 2 m n $
$ 15 m^4 n=5 m^2 n \cdot 3 m^2 $
$ -20 m^2 n^3=5 m^2 n \cdot-4 n^2$
Hence, $10 m^3 n^2+15 m^2 n-20 m^2 n^3$ can be factorised as $5 m^2 n\left(2 m n+3 m^2-4 n^2\right)$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The population of a city is $125000.$ If the annual birth rate and death rate are $5.5\%$ and $3.5\%$ respectively, calculate the population of city after $3$ years.
→Divide $-\text{x}^6+2\text{x}^4+4\text{x}^3+2\text{x}^2\text{ by }\sqrt{2}\text{x}^2.$
→A plot is in the form of a rectangle $ABCD$ having semi-circle on $BC$ as shown in Fig. If $AB = 60m$ and $BC = 28m,$ find the area of the plot.
→$\frac{\text{x}+1}{4}=\frac{\text{x}-2}{3}$
→Locate the points $A(1, 2), B (3, 4)$ and $C (5, 2)$ on a graph sheet taking suitable axes. Write the coordinates of the fourth point $D$ to complete the rhombus $ABCD.$ Measure the diagonals of this rhombus and find whether they are equal or not.
→The product of two rational numbers is $\frac{-16}{9}$. If one of the numbers is $\frac{-4}{3}$, find the other.
→Aman bought a shirt for Rs $374.50$ which includes $7\% VAT.$ Find the list price of the shirt.
→Find the greatest common factor of the polynomial:
$42 x^2 y z$ and $63 x^3 y^2 z^3$
→$42 x^2 y z$ and $63 x^3 y^2 z^3$
Verify Euler's relation for the following: A tetrahedron.
Subtract the sum of $(2x - x^2+ 5)$ and $(-4x - 3 + 7x^2)$ from $5.$
→