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Simplify: (x² - y²) / (x - y) * (x + y).
(x+y)2
x2+y2
x−y
1
(x+y)2
Recognize the numerator as the difference of squares identity to instantly factor and cancel out the common (x-y) term.
Algebraic expression: (x² - y²) / (x - y) * (x + y)
a2−b2=(a−b)(a+b)
Recognize the numerator as the difference of squares identity to instantly factor and cancel out the common (x-y) term.
Incorrectly canceling terms across operations without proper factorization or confusing (x+y)2 with x²⁺ʸ^2.
Factorize the Numerator
Use the standard algebraic difference of squares identity a2−b2=(a−b)(a+b) to expand the numerator x2−y2.
x2−y2=(x−y)(x+y)
Substitute and Cancel Terms
Substitute the factorized form into the expression, allowing the (x−y) term in the numerator and denominator to cancel out.
x−y(x−y)(x+y)×(x+y)=(x+y)×(x+y)
Multiply and Simplify
Multiply the remaining identical terms together to obtain the final simplified expression.
(x+y)2
A is correct because simplifying the expression yields (x+y)2.
Mastering fundamental algebraic identities speeds up polynomial factorization and quadratic expression simplification in competitive exams.
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