Question

please tell me the explanation of question no.12

Answer 1

${(x - \frac{2}{3}y)}^{3}$

We know that, (x - y)³ = x³ - 3x²y + 3xy² - y³

Here x = x, y = 2y/3

By substituting the values :

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

$= {x}^{3} - 2y( {x}^{2}) + 3x( \frac{4}{9} {y}^{2}) - \frac{8}{27} {y}^{3}$

$= {x}^{3} - 2x {y}^{2} + x( \frac{4}{3} {y}^{2} ) - \frac{8}{27} {y}^{3}$

$= {x}^{3} - 2x {y}^{2} + \frac{4}{3}x {y}^{2} - \frac{8}{27} {y}^{3}$

${( - 2x + 5y - 3z)}^{2}$

We know that, (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz.

Here x = -2x, y = 5y, z = -3z

By substituting the values :

$= {(-2x)}^{2} + {(5y)}^{2} + {(-3z)}^{2} + 2(-2x)(5y) + 2(5y)(-3z) + 2(-2x)(-3z)$

$= 4{x}^{2} + 25{y}^{2} + 9{z}^{2} - 20xy - 30yz + 12xz$