subtract -2x2+5xy+4y2 from the sum of x2-2xy+y2 and 3x2 +4xy-y2
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subtract -2x2+5xy+4y2 from the sum of x2-2xy+y2 and 3x2 +4xy-y2
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SolutioN:-
★ Sum of x² - 2xy + y² and 3x² + 4xy - y²:-
[tex] \sf \longrightarrow \: {x}^{2} - 2xy + {y}^{2} \: and \: 3{x}^{2} + 4xy - {y}^{2}[/tex]
[tex] \sf \longrightarrow \: ({x}^{2} - 2xy + {y}^{2}) \: + \: (3{x}^{2} + 4xy - {y}^{2})[/tex]
[tex] \sf \longrightarrow \: {x}^{2} - 2xy + {y}^{2} + 3{x}^{2} + 4xy - {y}^{2}[/tex]
[tex] \sf \longrightarrow \: {x}^{2} + 3{x}^{2} - 2xy+ 4xy + {y}^{2} - {y}^{2}[/tex]
[tex] \sf \longrightarrow \: {x}^{2} + 3{x}^{2} - 2xy+ 4xy + \cancel{{y}^{2} } - \cancel{{y}^{2}}[/tex]
[tex] \sf \longrightarrow \: 4{x}^{2} - 2xy+ 4xy + 0[/tex]
[tex] \sf \longrightarrow \: 4{x}^{2} + 2xy [/tex]
Now,
★ Substracting -2x² + 5xy +4y² from 4x² + 2xy:-
[tex] \sf \longrightarrow \: (4{x}^{2} + 2xy )- ( - 2 {x}^{2} + 5xy + 4 {y}^{2} )[/tex]
[tex] \sf \longrightarrow \: 4{x}^{2} + 2xy + 2 {x}^{2} - 5xy - 4 {y}^{2} [/tex]
[tex] \sf \longrightarrow \: 4{x}^{2} + 2 {x}^{2} + 2xy - 5xy - 4 {y}^{2} [/tex]
[tex] \sf \longrightarrow \: 6 {x}^{2} + 2xy - 5xy - 4 {y}^{2} [/tex]
[tex] \sf \longrightarrow \: 6 {x}^{2} - 3xy - 4 {y}^{2} [/tex]
[tex] \sf \longrightarrow \: 6 {x}^{2} - 4 {y}^{2} - 3xy [/tex]
Therefore:-
To subtract the expression -2x^2 + 5xy + 4y^2 from the sum of (x^2 - 2xy + y^2) and (3x^2 + 4xy - y^2), you can first calculate the sum of the two expressions and then subtract the given expression. Here's the step-by-step calculation:
Sum of (x^2 - 2xy + y^2) and (3x^2 + 4xy - y^2):
(x^2 - 2xy + y^2) + (3x^2 + 4xy - y^2)
Combine like terms:
x^2 + 3x^2 - 2xy + 4xy + y^2 - y^2
Simplify further:
(4x^2 + 2xy)
Now, subtract the expression -2x^2 + 5xy + 4y^2 from the above result:
(4x^2 + 2xy) - (-2x^2 + 5xy + 4y^2)
When you subtract, remember to distribute the negative sign:
4x^2 + 2xy + 2x^2 - 5xy - 4y^2
Combine like terms:
(4x^2 + 2x^2) + (2xy - 5xy) - 4y^2
Further simplification:
6x^2 - 3xy - 4y^2
So, the result of subtracting -2x^2 + 5xy + 4y^2 from the sum of (x^2 - 2xy + y^2) and (3x^2 + 4xy - y^2) is 6x^2 - 3xy - 4y^2.