Question

What should be added to 2x^2 + xy – y^2to get 4x^2 + 8xy ?

Answer 1

Step-by-step explanation:

Given that:-

Let the required number=A

A should be added to 2x²+xy-y² to get 4x²+8xy

=>2x²+xy-y²+A=4x²+8xy

=>A=(4x²+8xy)-(2x²+xy-y²)

=>A=4x²+8xy-2x²-xy+y²

=>A=(4x²-2x²)+(8xy-xy)+y²

=>A=2x²+7xy+y²

The required answer is 2x²+7xy+y²

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Let the term should be 'X' which be added to $\sf 2 {x}^{2} + xy - {y}^{2}$ to get $\sf 4 {x}^{2} + 8xy$

According to the question:-

$\sf= > 2 {x}^{2} + xy - {y}^{2} + X= 4 {x}^{2} + 8xy$

Here,the term $2 {x}^{2} + xy - {y}^{2}$is added on left hand side when it shift towards the other side it's sign gets changed from +ve to -ve.

$\sf = > X = 4 {x}^{2} + 8xy - (2 {x}^{2} + xy - {y}^{2} )$

$\sf= > X= 4 {x}^{2} + 8xy - 2 {x}^{2} - xy + {y}^{2}$

$\sf= > X = 2 {x}^{2} + 7xy + {y}^{2}$

$\therefore$$\sf 2 {x}^{2} + 7xy + {y}^{2}$should be added to $\sf 2 {x}^{2} + xy - {y}^{2}$ to get $\sf = 4 {x}^{2} + 8xy$

Check:

$\sf= > 2 {x}^{2} + xy - {y}^{2} + 2{x}^{2} + 7xy+{y}^{2}$=$\sf 4{x}^{2} + 8xy$