Question

$\red\huge{QUESTION::}$

MULTIPLY THE BIONOMIAL

$( \frac{3}{4} {a}^{2} + 3 {b}^{2} )and \: 4( {a}^{2} - \frac{2}{3} {b}^{2} )$
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Answer 1

Answer:

$given \: \: bionomal \: \: = > \\ \\ ( \frac{3}{4} {a}^{2} + 3 {b}^{2} ) \: \: \: and \: \: 4( {a}^{2} - \frac{2}{3} {b}^{2} ) \\ \\ multiplication \: \: = > \\ \\ 3 {a}^{4} - 2 {a}^{2} {b}^{2} + 12 {a}^{2} {b}^{2} - 8 {b}^{4}$

Answer 2

Answer:

$\red {( \frac{3}{4} {a}^{2} + 3 {b}^{2} )\times \: 4( {a}^{2} - \frac{2}{3} {b}^{2} )}$

$\green {= 3a^{4} + 10a^{2}b^{2}-8b^{4} }$

Step-by-step explanation:

$( \frac{3}{4} {a}^{2} + 3 {b}^{2} )\times \: 4( {a}^{2} - \frac{2}{3} {b}^{2} )$

$= 3\left( \frac{a^{2}}{4} + b^{2}\right) \times 4( {a}^{2} - \frac{2}{3} {b}^{2} )$

$3\left( \frac{a^{2}+4b^{2}}{4} \right) \times 4\left(\frac{3a^{2}-2b^{2}}{3}\right)$

$= \frac{3}{4} \times \frac{4}{3} \left(a^{2}+4b^{2}\right)\left(3a^{2}-2b^{2}\right)$

$= a^{2}\left(3a^{2}-2b^{2}\right)+4b^{2}\left(3a^{2}-2b^{2}\right)$

$\pink { ( By \:distributive \:property)}$

$= 3a^{4} - 2a^{2}b^{2} + 12a^{2}b^{2}-8b^{4}$

$= 3a^{4} + 10a^{2}b^{2}-8b^{4}$

Therefore.,

$\red {( \frac{3}{4} {a}^{2} + 3 {b}^{2} )\times \: 4( {a}^{2} - \frac{2}{3} {b}^{2} )}$

$\green {= 3a^{4} + 10a^{2}b^{2}-8b^{4} }$

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