Question

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

Answer 1

Answer:

Step-by-step explanation:

Formula used:

$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$

Now,

$(\sqrt{2}x+2y-\sqrt{3}z)^2\\\\=[\sqrt{2}x+2y+(-\sqrt{3}z)]^2\\\\=(\sqrt{2}x)^2+(2y)^2+(-\sqrt{3}z)^2+2(\sqrt{2}x)(2y)+2(2y)(-\sqrt{3}z)+2(-\sqrt{3}z)(\sqrt{2}x)\\\\=2x^2+4y^2+3z^2+4\sqrt{2}xy-4\sqrt{3}yz-2\sqrt{2}\sqrt{3}zx$

Answer 2

Solution:

As we know that

$( {a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ \\ so \\ \\ ( { \sqrt{2} x + 2y - \sqrt{3}z )}^{2} = \\ \\ ({\sqrt{2} x})^{2} + ({2y})^{2} + ({\sqrt{3}z})^{2} + 2( \sqrt{2}x)(2y) \\ \\ + 2(2y)( - \sqrt{3} z) + 2( - \sqrt{3}z) ( \sqrt{2}x)\\ \\ = 2 {x}^{2} + 4 {y}^{2} + 3 {z}^{2} + 4 \sqrt{2} xy - 4 \sqrt{3} yz - 2 \sqrt{6}xz$
Hope it helps you.