Question

answer of 6th question<br />

Answer 1

Since we have to multiply here, let's open the brackets.

$( \frac{3}{4} {a}^{2} + 3 {b}^{2} )(4 {a}^{2} - \frac{5}{3} {b}^{2} )$

$= > \frac{3}{4} {a}^{2} (4 {a}^{2} - \frac{5}{3} {b}^{2} ) + 3 {b}^{2} (4 {a}^{2} - \frac{5}{3} {b}^{2} )$

Now multiply 3a²/4 with 4a² and -5b²/3

and multiply 3b² with 4a² and -5b²/3

So,
$= > \frac{3}{4 } {a}^{2} \times 4 {a}^{2} + \frac{3}{4} {a}^{2} \times ( \frac{ - 5}{3} {b}^{2} ) + 3 {b}^{2} \times 4 {a}^{2} + 3 {b}^{2} \times \frac{ - 5}{3} {b}^{2} \\ = > 3 {a}^{4} - \frac{5}{4} {a}^{2} {b}^{2} + 12 {a}^{2} {b}^{2} - 5 {b}^{4}$
Now add the like terms

=>
$3 {a}^{4 } - \frac{5}{4} {a}^{2} {b}^{2} + \frac{48}{4} {a}^{2} {b}^{2} - 5 {b}^{4} \\ \\ = > 3 {a}^{4} + \frac{43}{4} {a}^{2} {b}^{2} - 5 {b}^{4}$
Hope it helps dear friend ☺️