Question

Evaluate each of the following using identities. a)
$( \frac{2}{3} p - \frac{3}{4} q) {}^{2}$
​

Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\therefore \left( \dfrac{2}{3} p - \dfrac{3}{4} q \right)^2$

$\sf\implies \left( \dfrac{2}{3} p - \dfrac{3}{4} q \right)^2$

✯IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: (a-b)^2=a^2+b^2-2ab\:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\sf\implies \bigg( \dfrac{2p}{3} \bigg)^2 + \bigg( \dfrac{3q}{4} \bigg) - 2 \times \bigg( \dfrac{2p}{3} \bigg) \times \bigg( \dfrac{3q}{4}\bigg)$

$\sf\implies \dfrac{4p^2}{9} + \dfrac{9q^2}{16} - \dfrac{12pq}{12}$

$\sf\implies \dfrac{4p^2}{9} + \dfrac{9q^2}{16} - \dfrac{\cancel{12}\:pq}{\cancel{12}}$

$\sf\implies \dfrac{4p^2}{9} + \dfrac{9q^2}{16} - pq$

$\sf\implies \dfrac{64p^2+81q^2}{144} - pq$

$\sf\implies \dfrac{64p^2+81q^2-144pq}{144}$

$\large{\boxed{\bf{ \star\:\: \dfrac{64p^2+81q^2-144pq}{144}\:\: \star}}}$

________________

Answer 2

$\large\underline{\underline{\bold{\pink{\mathfrak{AnSwEr}}}}}$

$\large\underline\bold{GIVEN,}$

$\sf\therefore \left( \dfrac{2}{3} p - \dfrac{3}{4} q \right)^2$

$\sf\implies \left( \dfrac{2}{3} p - \dfrac{3}{4} q \right)^2$

iDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: (a-b)^2=a^2+b^2-2ab\:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\sf\implies \bigg( \dfrac{2p}{3} \bigg)^2 + \bigg( \dfrac{3q}{4} \bigg) - 2 \times \bigg( \dfrac{2p}{3} \bigg) \times \bigg( \dfrac{3q}{4}\bigg)$

$\sf\implies \dfrac{4p^2}{9} + \dfrac{9q^2}{16} - \dfrac{12pq}{12}$

$\sf\implies \dfrac{4p^2}{9} + \dfrac{9q^2}{16} - \dfrac{\cancel{12}\:pq}{\cancel{12}}$

$\sf\implies \dfrac{4p^2}{9} + \dfrac{9q^2}{16} - pq$

$\sf\implies \dfrac{64p^2+81q^2}{144} - pq$

$\sf\implies \dfrac{64p^2+81q^2-144pq}{144}$

$\large{\boxed{\bf{ \star\:\: \dfrac{64p^2+81q^2-144pq}{144}\:\: \star}}}$