Question

If m = 9x2 - 4xy + 5y2 and n = - 3x2 + 2xy - y2, find :
(i) 2m - n
(ii) m + 2n
(iii) m - 3n.​

Answer 1

Answer:

Answer in attachment pls see

Hope it helps you

Pls mark Brainlliest✨

Answer 2

Answer:

(i) $2m-n=21x^2- 10xy + 11y^2$  

(ii) $m+2n=3\big(x^2 + y^2\big)$

(iii) $m-3n=18x^2 - 10xy + 8y^2$

Step-by-step explanation:

Given the equations:

$m = 9x^2 - 4xy + 5y^2$ and $n = - 3x^2 + 2xy - y^2$

(i) $2m-n$

Substituting the given equations,

$2\big( 9x^2 - 4xy + 5y^2\big)-\big( - 3x^2 + 2xy - y^2\big)$

Opening the brackets

$18x^2 - 8xy + 10y^2+3x^2- 2xy + y^2$

Grouping the like terms

$18x^2 +3x^2- 8xy - 2xy + 10y^2+ y^2$

$= 21x^2- 10xy + 11y^2$

(ii) $m+2n$

Substituting the given equations,

$9x^2 - 4xy + 5y^2+2\big( - 3x^2 + 2xy - y^2\big)$

Opening the brackets

$9x^2 - 4xy + 5y^2 - 6x^2 + 4xy -2 y^2$

Grouping the like terms

$9x^2 - 6x^2 - 4xy + 4xy+ 5y^2 -2 y^2$

$= 3x^2 + 3 y^2=3\big(x^2 + y^2\big)$

(iii) $m-3n$

Substituting the given equations,

$9x^2 - 4xy + 5y^2-3\big( - 3x^2 + 2xy - y^2\big)$

Opening the brackets

$9x^2 - 4xy + 5y^2+9x^2 - 6xy +3y^2$

Grouping the like terms

$9x^2+9x^2 - 4xy - 6xy + 5y^2 +3y^2$

$=18x^2 - 10xy + 8y^2$

Therefore, (i) $2m-n=21x^2- 10xy + 11y^2$  

(ii) $m+2n=3\big(x^2 + y^2\big)$ and  (iii) $m-3n=18x^2 - 10xy + 8y^2$

For more problems:

https://brainly.in/question/5254169

https://brainly.in/question/7639599