Question

Solve the following problems:
a) Simplify: [@)x2 + ?)y2] x [3x2 – 4y21
2​

Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt Simplify$

$\sf \bf \Bigg[\bigg(\dfrac{3}{2}\bigg){x}^{2}+\bigg(\dfrac{2}{5}\bigg){y}^{2}\Bigg] \times \Bigg[3{x}^{2}-4{y}^{2}\Bigg]$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf\implies \Bigg[\bigg(\dfrac{3}{2}\bigg){x}^{2}+\bigg(\dfrac{2}{5}\bigg){y}^{2}\Bigg] \times \Bigg[3{x}^{2}-4{y}^{2}\Bigg]$

$\sf \bf\implies \Bigg[\bigg(\dfrac{3{x}^{2}}{2}\bigg) +\bigg(\dfrac{2{y}^{2}}{5}\bigg)\Bigg] \times \Bigg[3{x}^{2}-4{y}^{2}\Bigg]$

$\sf \bf\implies \Bigg[\dfrac{3{x}^{2}}{2} +\dfrac{2{y}^{2}}{5}\Bigg] \times \Bigg[3{x}^{2}-4{y}^{2}\Bigg]$

$\sf \bf\implies 3{x}^{2} \times \Bigg[\dfrac{3{x}^{2}}{2} +\dfrac{2{y}^{2}}{5}\Bigg] - 4{y}^{2}\times \Bigg[\dfrac{3{x}^{2}}{2} +\dfrac{2{y}^{2}}{5}\Bigg]$

$\sf \bf \implies \dfrac{9{x}^{4}}{2}+\dfrac{6{x}^{2}{y}^{2}}{5}-\dfrac{12{x}^{2}{y}^{2}}{2}-\dfrac{8{y}^{4}}{5}$

$\sf \bf \implies \dfrac{9{x}^{4}}{2}+\dfrac{12{x}^{2}{y}^{2}-60{x}^{2}{y}^{2}}{10}-\dfrac{8{y}^{4}}{5}$

$\sf \bf \implies \dfrac{9{x}^{4}}{2}+\dfrac{-48{x}^{2}{y}^{2}}{10}-\dfrac{8{y}^{4}}{5}$

$\implies{\boxed {\color{blue} {\sf \bf \dfrac{9{x}^{4}}{2}-\dfrac{48{x}^{2}{y}^{2}}{10}-\dfrac{8{y}^{4}}{5}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

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$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

${\underbrace {\overbrace {\tt Identities}}}$

$\sf \bf {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}$

$\sf \bf {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}$

$\sf \bf (a+b) (a-b) ={a}^{2}-{b}^{2}$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$