Question

pls send all answers​

Answer 1

Simplify :-

i) x ( y - z ) + y ( z - x ) + z ( x - y )

$\implies\sf xy - xz + yz - yx + zx - zy$

$\implies\sf \cancel{xy} - \cancel{xy} + \cancel{xz} - \cancel{xz} + \cancel{yz} - \cancel{yz}$

$\boxed{\implies\sf0}$

ii) ( x² + x + 1 )( x² - x + 1 ) and find it's value for x = 1

$\implies\sf x^2 ( x^2 - x + 1 ) + x ( x^2 - x + 1 ) + 1 ( x^2 - x + 1 )$

$\implies\sf x^4 - \cancel{x^3} + \cancel{x^2} + \cancel{x^3} - \cancel{x^2} +\cancel x + x^2 - \cancel x + 1$

$\implies\sf x^4 + x^2 + 1$

Substituting value of x as x = 1

$\implies\sf 1^4 + 1^2 + 1$

$\boxed{\implies\sf 3 }$

$\sf iii) \dfrac{40x^4y^5 + 72 x^5y^7}{8x^2y}$

$\implies\sf \dfrac{40x^4y^5}{8x^2y} + \dfrac{72x^5y^7}{8x^2y}$

$\implies\sf 5 \times x^{4-2} \times y^{5-1} + 9 \times x^{5-2} \times y^{7-1}$

$\boxed{\implies\sf 5x^2y^4 + 9x^3y^6}$

$\sf iv) \dfrac{7.63 \times 7.63 - 2.37 \times 2.37}{5.26}$

Using the identity -

• $\sf a^2 - b^2 = (a + b)(a - b)$

$\implies\sf \dfrac{(7.63 + 2.37)(7.63 - 2.37)}{5.26}$

$\implies\sf \dfrac{10 \times \cancel{5.26}}{\cancel{5.26}}$

$\boxed{\implies\sf 10}$

Factorize :-

$\sf i) 49(x-y)^2 - 25(x+y)^2$

$\implies\sf [7(x-y)]^2 - [5(x+y)]^2$

• $\sf a^2 - b^2 = ( a + b )(a-b)$

$\implies\sf [7(x - y) + 5(x+ y)][7(x-y)- 5(x+y)]$

$\implies\sf ( 7x - 7y + 5x + 5y )( 7x - 7y - 5x - 5y)$

$\implies\sf ( 12x - 2y )( 2x - 12y )$

$\implies\sf 2 ( 6x - y ) \times 2 ( x - 6y )$

$\implies\sf 4 ( 6x - y ) ( x - 6y )$

$\boxed{\sf 49(x-y)^2 - 25(x+y)^2 = 4 ( 6x - y ) ( x - 6y )}$

$\sf ii) x^2 - y^2 - x - y$

$\implies\sf (x + y)(x - y) - x - y$

$\implies\sf (x + y)(x - y) - ( x + y )$

$\implies\sf (x + y)[x - y - 1]$

$\boxed{\sf x^2 - y^2 - x - y = (x + y)[x - y - 1]}$