Simplify the expression-12pq-2p-3q2 -2p-3q2

Given: nbsp;12pq/(2p+3q)^2 (2p 3q)^2 By using the identities, nbsp; (a+b)^2 = a^2+2ab +b^2 (a b)^2 = a^2 2ab+b^2 the denominator can be simplified as ...

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Byju's Answer

Standard VIII

Mathematics

(x+y)^2 + (x-y)^2 and (x+y)^2 - (x-y)^2

Simplify the ...

Question

Simplify the expression:
$\frac{12 p q}{(2 p + 3 q)^{2} - (2 p - 3 q)^{2}}$

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Solution

Given: $\frac{12 p q}{(2 p + 3 q)^{2} - (2 p - 3 q)^{2}}$

By using the identities,
$(a + b)^{2} = a^{2} + 2 a b + b^{2} (a - b)^{2} = a^{2} - 2 a b + b^{2}$

the denominator can be simplified as
$(2 p + 3 q)^{2} - (2 p - 3 q)^{2} = 4 p^{2} + 9 q^{2} + 12 p q - (4 p^{2} + 9 q^{2} - 12 p q) = 4 p^{2} + 9 q^{2} + 12 p q - 4 p^{2} - 9 q^{2} + 12 p q = 24 p q$

The the given expression becomes,
$\frac{12 p q}{(2 p + 3 q)^{2} - (2 p - 3 q)^{2}} = \frac{12 p q}{24 p q} = \frac{1}{2}$

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Similar questions

State whether the following statement is true or false:

{(2 p - 3 q)}^{2}

4 p^{2} + 9 q^{2} - 12 p q

Q. Using the identity

(a + b)^{2} = a^{2} + 2 a b + b^{2}

, simplify

(2 p + 3 q)^{2}

Q. If

2 p + 3 q = 18

and

4 p^{2} + 4 p q - 3 q^{2} - 36 = 0

then what is

(2 p + q)

equal to?

Q. Expand.

(i) ( 5a + 6b)² (ii)

{(\frac{a}{2} + \frac{b}{3})}^{2}

(iii)

{(2 p - 3 q)}^{2}

(iv)

{(x - \frac{2}{x})}^{2}

(v)

{(a x + b y)}^{2}

(vi)

{(7 m - 4)}^{2}

(vii)

{(x + \frac{1}{2})}^{2}

(viii)

{(a - \frac{1}{a})}^{2}

Q. IF

3 p^{2} = 5 p + 2

and

3 q^{2} = 5 q + 2

where

p \neq q

, then the equation whose roots are

3 p - 2 q

and

3 q - 2 p

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Simplify the expression: 12pq(2p+3q)2−(2p−3q)2

Given: 12pq(2p+3q)2−(2p−3q)2 By using the identities, (a+b)2=a2+2ab+b2(a−b)2=a2−2ab+b2 the denominator can be simplified as (2p+3q)2−(2p−3q)2=4p2+9q2+12pq−(4p2+9q2−12pq)=4p2+9q2+12pq−4p2−9q2+12pq=24pq The the given expression becomes, 12pq(2p+3q)2−(2p−3q)2=12pq24pq=12

Simplify the expression:
$\frac{12 p q}{(2 p + 3 q)^{2} - (2 p - 3 q)^{2}}$