The reduced form of $36 x^{2}-81 y^{2}$ is
i$(6 x+9 y)(6 x-9 y) $
ii$(6 x+9 y)(4 x-5) $
iii.$(9 x+6 y)(9 x-6 y)$
iv. $(9 y-6 x)(9 y+6 x) $
To do: Find the reduced for of $36 x^{2}-81 y^{2}$
Solution:
$36x^{2} - 81y{2}$
= $(6x)^{2} - (9y)^{2}$
Using Identity
$x^{2} - y^{2} = (x + y)(x - y)$
$36x^{2} - 81y^{2}$
= $(6x)^{2} - (9y)^{2} = (6x + 9y) (6x - 9y)$
So option (i) (6x + 9y) (6x - 9y) is CORRECT
- Related Articles
- Factorize:$4(x - y)^2 - 12(x -y) (x + y) + 9(x + y)^2$
- Factorise the following using appropriate identities:(i) \( 9 x^{2}+6 x y+y^{2} \)(ii) \( 4 y^{2}-4 y+1 \)(iii) \( x^{2}-\frac{y^{2}}{100} \)
- Multiply:$(x^6-y^6)$ by $(x^2+y^2)$
- Factorize:$2(x+y)^2 - 9(x+y) -5$
- Simplify:\( 4(x+y)-6(x+y)^{2} \)
- If X = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9} and Y = {3 , 6 , 9 , 12 , 15 , 18} , find $(X - Y)$ and $(Y -X)$ and illustrate them in Venn diagram.
- Factorize:\( x^{3}-2 x^{2} y+3 x y^{2}-6 y^{3} \)
- Solve the following system of equations: $\frac{x}{7}\ +\ \frac{y}{3}\ =\ 5$ $\frac{x}{2}\ –\ \frac{y}{9}\ =\ 6$
- Add the following algebraic expressions.a) \( x+5 \) and \( x+3 \)b) \( 3 x+4 \) and \( 4 x+9 \)c) \( 5 y-2 \) and \( 2 y+7 \) d) \( 8 y-3 \) and \( 5 y-6 \)
- Solve the following system of equations by the method of cross-multiplication: $\frac{57}{(x\ +\ y)}\ +\ \frac{6}{(x\ –\ y)}\ =\ 5$ $\frac{38}{(x\ +\ y)}\ +\ \frac{21}{(x\ –\ y)}\ =\ 9$
- Find the products of the following monomials.a. \( (-6) x^{2} \times 7 x y \)b. \( 2 a b \times(-6) a b \)c. \( \left(-4 x^{2} y^{2}\right) \times 3 x^{2} y^{2} \)d. \( 9 x y z \times 2 z^{3} \)
- Solve the following pairs of equations by reducing them to a pair of linear equations:(i) \( \frac{1}{2 x}+\frac{1}{3 y}=2 \)\( \frac{1}{3 x}+\frac{1}{2 y}=\frac{13}{6} \)(ii) \( \frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2 \)\( \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1 \)(iii) \( \frac{4}{x}+3 y=14 \)\( \frac{3}{x}-4 y=23 \)(iv) \( \frac{5}{x-1}+\frac{1}{y-2}=2 \)\( \frac{6}{x-1}-\frac{3}{y-2}=1 \)(v) \( \frac{7 x-2 y}{x y}=5 \)\( \frac{8 x+7 y}{x y}=15 \),b>(vi) \( 6 x+3 y=6 x y \)\( 2 x+4 y=5 x y \)4(vii) \( \frac{10}{x+y}+\frac{2}{x-y}=4 \)\( \frac{15}{x+y}-\frac{5}{x-y}=-2 \)(viii) \( \frac{1}{3 x+y}+\frac{1}{3 x-y}=\frac{3}{4} \)\( \frac{1}{2(3 x+y)}-\frac{1}{2(3 x-y)}=\frac{-1}{8} \).
- Solve the following pair of equations by reducing them to a pair of linear equations$ 6 x+3 y=6 x y $$2 x+4 y=5 x y $
- Factorise:\( 4 x^{2}+9 y^{2}+16 z^{2}+12 x y-24 y z-16 x z \)
- From the choices given below, choose the equation whose graphs are given in Fig. \( 4.6 \) and Fig. 4.7.For Fig. 4. 6(i) \( y=x \)(ii) \( x+y=0 \)(iii) \( y=2 x \)(iv) \( 2+3 y=7 x \)For Fig. \( 4.7 \)(i) \( y=x+2 \)(ii) \( y=x-2 \)(iii) \( y=-x+2 \)(iv) \( x+2 y=6 \)"\n
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies