Answer :
The given algebraic equation formula i.e., [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b of -3 and -5 respectively.
As per the question statement, we are supposed to verify the algebraic equation formula
[tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex]
We are given that a = -3 and b = -5
Now substituting the values of a and b in the algebraic equation formula
[tex](a^{2} -b^{2} )=(a+b)(a-b)\\LHS = (a^{2} -b^{2} )\\LHS= ([-3]^{2} -[-5]^{2} )\\LHS=(9-25)\\LHS = -16[/tex]
LHS = Left hand side of the equation
Now considering RHS i.e., Right hand side
[tex]RHS = (a+b)(a-b)\\RHS = ([-3]+[-5])([-3]-[-5])\\RHS= (-8)(2)\\RHS = -16[/tex]
As Left Hand Side LHS = Right Hand Side RHS
Hence the equation, [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b and is true for all real values of a and b.
- Algebraic Equation: The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, root operations.
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