-STEP explanation:\sf \: (i) \: ( \frac{3}{4} {a}^{2} + {3b}^{2} ) \: and \: 4( {a}^{2} - \frac{2}{3} {b}^{2} )(i)( 43 a 2 +3b 2 )and4(a 2 − 32 b 2 )\sf \: = > \: ( \frac{3}{4} {a}^{2} + {3b}^{2} ) \: \TIMES \: 4( {a}^{2} - \frac{2}{3} {b}^{2} ) \: \: \:=>( 43 a 2 +3b 2 )×4(a 2 − 32 b 2 )\sf \: \sf = ( \frac{3}{4} {a}^{2} + 3 {b}^{2} ) \: \times [(4 \times {a}^{2}) - (4 \times \frac{2}{3} {b}^{2} ) ]=( 43 a 2 +3b 2 )×[(4×a 2 )−(4× 32 b 2 )]\sf \: = ( \frac{3}{4} a² + 3b²) × (4a² - \frac{8}{3} b²)=( 43 a²+3b²)×(4a²− 38 b²)\sf \: = \: \frac{3}{4} {a}^{2} (4 {a}^{2} - \frac{8}{3} {b}^{2} ) + 3 {b}^{2} ( {4a}^{2} - \frac{8}{3} {b}^{2} )= 43 a 2 (4a 2 − 38 b 2 )+3b 2 (4a 2 − 38 b 2 )\sf \: = ( \frac{3}{4} {a}^{2} \times {4a}^{2} ) - (\frac{3}{4} {a}^{2} \times \frac{8}{3} {b}^{2} ) + ( {3b}^{2} \times {4a}^{2} ) - ( {3b}^{2} \times \frac{8}{3} {b}^{2} )=( 43 a 2 ×4a 2 )−( 43 a 2 × 38 b 2 )+(3b 2 ×4a 2 )−(3b 2 × 38 b 2 )\sf \: = 3 {a}^{4} - 2a²b² + 12b²a²-8b4=3a 4 −2a²b²+12b²a²−8b4\begin{gathered} \\ \\ \\ \end{gathered} \sf \: (ii) \: \: \:( y - 8) \: \: and \: \: \: (3y - 4) \: \:(ii)(y−8)and(3y−4)\begin{gathered} \sf \: = y(3y - 4) - 8(3y - 4) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf= (y \times 3y) - (y \times 4) - (8 \times 3y) + (8 \times 4) \\ \sf= 3y² - 4y + 24y - 32 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \: = 3y² - 28y + 32 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered} =y(3y−4)−8(3y−4)=(y×3y)−(y×4)−(8×3y)+(8×4)=3y²−4y+24y−32=3y²−28y+32 -----------------------------------------------------------THEREFORE your answer is(i) = 3a⁴ - 2a²b² + 12b²a²-8b⁴(ii) = 3y² - 28y + 32