Question

expand the following,using suitable identity(√2x+2y-√3z)²

Answer 1

${\big( \sqrt{2} x + 2y - \sqrt{3} z \big)}^{2} \\ \\ = {( \sqrt{2} x)}^{2} + {(2y)}^{2} + {( \sqrt{3} z)}^{2} \\ \: \: \: \: \: + 2 \big( \sqrt{2} x \times 2y - 2y \times \sqrt{3} z - \sqrt{3} z \times \sqrt{2} x \big) \\ \\ = 2 {x}^{2} + 4 {y}^{2} + 3 {z}^{2} + 2\big(2 \sqrt{2} xy - 2 \sqrt{3} yz - \sqrt{6} xz \big) \\ \\ = 2 {x}^{2} + 4 {y}^{2} + 3 {z}^{2} + 4 \sqrt{2} xy - 4 \sqrt{3} yz - 2\sqrt{6} xz$

Answer 2

Step-by-step explanation:

$\begin{lgathered}{\big( \sqrt{2} x + 2y - \sqrt{3} z \big)}^{2} \\ \\ = {( \sqrt{2} x)}^{2} + {(2y)}^{2} + {( \sqrt{3} z)}^{2} \\ \: \: \: \: \: + 2 \big( \sqrt{2} x \times 2y - 2y \times \sqrt{3} z - \sqrt{3} z \times \sqrt{2} x \big) \\ \\ = 2 {x}^{2} + 4 {y}^{2} + 3 {z}^{2} + 2\big(2 \sqrt{2} xy - 2 \sqrt{3} yz - \sqrt{6} xz \big) \\ \\ = 2 {x}^{2} + 4 {y}^{2} + 3 {z}^{2} + 4 \sqrt{2} xy - 4 \sqrt{3} yz - 2\sqrt{6} xz\end{lgathered}$