Question

please answer this 2 questions​

Answer 1

Answer:

$1) \: \: (3 + \sqrt{2)} (2 + \sqrt{3)}$

$= 3(2 + \sqrt{3)} + \sqrt{2} (2 + \sqrt{3} )$

$= 6 + 3 \sqrt{3} + 2 \sqrt{2} + \sqrt{6}$

$2) \: \: (4 + \sqrt{3} )(4 - \sqrt{3} )$

We know that,

(a+b) (a-b) =a²-b²

$= {(4)}^{2} - {( \sqrt{3}) }^{2}$

$= 16 - 3$

$= 13$

$3) \: \: {( \sqrt{3 } + \sqrt{2} )}^{2}$

We know that,

(a+b) ²=a²+b²+2ab

$= {( \sqrt{3}) }^{2} + {( \sqrt{2} )}^{2} + 2 \times \sqrt{3 } \times \sqrt{2}$

$= 3 + 2 + 2 \sqrt{6}$

$= 5 + 2 \sqrt{6}$

$4)8 {x}^{3} + 27 {y}^{3} + 36 {x}^{2} y + 54x {y}^{2}$

$= {(2x)}^{3} + {(3y)}^{3} + 3 {(2x)}^{2} \times 3y + 3 \times 2x(3y) {}^{2}$

We know that,

(a+b) ³=a³+b³+3a²b+3ab²

$= {(2x + 3y)}^{3}$

$= (2x + 3y)(2x + 3y)(2x + 3y)$

$5)4 {x}^{2} + {y}^{2} + {z}^{2} + 4xy + 2yz + 4xz$

$= {(2x)}^{2} + {(y)}^{2} + {(z)}^{2} + 2 \times 2x \times y + 2 \times y \times z + 2 \times 2x \times z$

We know that,

(a+b+c) ²=a²+b²+c²+2ab+2bc+2ca

$= {(2x + y + z)}^{2}$

$= (2x + y + z)(2x + y + z)$