Question

Multiply the binomial

Answer 1

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!}}}$

$= \frac{3}{4} a {}^{2} \times 4(a {}^{2} - \frac{2b {}^{2} }{3} ) + 3b {}^{2} \times 4(a {}^{2} - \frac{2b {}^{2} }{3} ) \\ = 3a {}^{4} - 2a {}^{2} b {}^{2} + 12a {}^{2} b {}^{2} - 8b {}^{4} \\ = 3a {}^{4} + 10a {}^{2} b {}^{2} - 8b {}^{4}$
Hope it helps you

Answer 2

Multiplication is a process in which two or more numerals or variables are multiplied with each other so as to obtain a single product.


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

Now we can simply multiply the given terms,

${a}^{2} ( {3a}^{2} - {2b}^{2} ) + {4b}^{2} ( {3a}^{2} - {2b}^{2} ) \\ \\ {a}^{4} - {2a}^{2} {b}^{2} + {12a}^{2} {b}^{2} - {8b}^{4} \\ \\ {a}^{4} + {10a}^{2} {b}^{2} - {8b}^{4}$