Question
Show that: $(4 p q+3 q)^2-(4 p q-3 q)^2=48 p q^2$
✓
Answer
$(4 p q+3 q)^2-(4 p q-3 q)^2=48 p q^2$
LHS $= (4pq + 3q)^2- (4pq - 3q)^2$
$= 4(4pq) (3q) [∵(a + b)^2- (a + b)^2= 4ab]$
$= 48pq^2$
= RHS
LHS $= (4pq + 3q)^2- (4pq - 3q)^2$
$= 4(4pq) (3q) [∵(a + b)^2- (a + b)^2= 4ab]$
$= 48pq^2$
= RHS
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
Express the following numbers as the sum of odd numbers using the pattern given below
(i) $6^3$$\quad$(ii) $8^3$$\quad$(iii) $7^3$
$\begin{array}{r}1=1=1^3 \\ 3+5=8=2^3 \\ 7+9+11=27=3^3 \\ 13+15+17+19=64=4^3 \\ 21+23+25+27+29=125=5^3\end{array}$
→(i) $6^3$$\quad$(ii) $8^3$$\quad$(iii) $7^3$
$\begin{array}{r}1=1=1^3 \\ 3+5=8=2^3 \\ 7+9+11=27=3^3 \\ 13+15+17+19=64=4^3 \\ 21+23+25+27+29=125=5^3\end{array}$
Draw the net of the following shape. 
Show that:
$ (3 x+7)^2-84 x=(3 x-7)^2 $
→$ (3 x+7)^2-84 x=(3 x-7)^2 $
Aman's income is $20\%$ less than that of Anil. How much percent is Anil's income more than Aman's income$?$
→By what least number should the given number be multiplied to get a perfect square number$?$ In case, find the number whose square is the new number. $2925$
→Using suitable identities, evaluate the following.
$(729)^2- (271)^2$
→$(729)^2- (271)^2$
Solve:
$4x^4+ 1$
→$4x^4+ 1$
Find the square root in decimal form: $236.144689$
→Find the following products: $\frac{-7}{6}\times24$
→The measure of angles of a hexagon are $x^\circ , (x - 5)^\circ (x - 5)^\circ , (2x - 5)^\circ , (2x - 5)^\circ , (2x + 20)^\circ .$ Find the value of $x.$
→