Maths-
General
Easy
Question
Fundamental Algebra:
1. Add:
(i) x^{2} – y^{2} – 1 ; y^{2} – 1 – x^{2} ; 1 – x^{2} – y^{2}
Hint:
- The concept used in this question is the addition of polynomials.
○ Arrange the term in the decreasing order of their power.
○ To add polynomials simply add any like terms together.
○ Like terms are terms whose variables and exponents are the same
The correct answer is: - ( x2 + y2 + 1 )
Answer:
- Step by step explanation:
○ Given:
Expression: x^{2} – y^{2} – 1 ;
y^{2} – 1 – x^{2} ;
1 – x^{2} – y^{2}
○ Step 1:
○ Simplify the expression.
( x^{2} – y^{2} – 1 ) + ( y^{2} – 1 – x^{2} ) + ( 1 – x^{2} – y^{2} )
( x^{2} – y^{2} – 1 ) + ( y^{2} – 1 – x^{2} ) + ( 1 – x^{2} – y^{2} )
○ Step 2:
○ Group the like terms.
( x^{2} – x^{2} – x^{2} ) + ( y^{2} – y^{2}– y^{2} ) + ( 1 – 1 – 1 )
( – x^{2} ) + ( – y^{2} ) + ( – 1 )
○ Step 3:
○ Take -1 common from all terms,
- ( x^{2} + y^{2} + 1 )
- Final Answer:
- ( x^{2} + y^{2} + 1 )
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