सङ्कलन-व्यवकलनाभ्यां
Sankalana-vyavakalanābhyām – “By addition and subtraction”
Simplify algebraic expressions using conjugate pairs and rational identities
What does it mean?
This sutra is used to simplify algebraic expressions by applying the identity:
(a + b)(a - b) = a² - b²
It’s especially helpful when working with conjugate pairs or rational expressions that
can be reduced using addition and subtraction.
The Method
- Start with an expression like:
-
(x + y)(x - y) - Apply the
identity:
(x + y)(x - y) = x² - y² - Now try a
rational example:
[(x + y)(x - y)] / [(x + y) - (x - y)] - Numerator
becomes:
x² - y² - Denominator simplifies to:
2y - Final simplified expression:
(x² - y²) / 2y
Why it matters
This sutra helps you recognize algebraic patterns and reduce complex expressions quickly. It’s especially useful in competitive exams where speed and accuracy matter. By mastering this, you can simplify rational expressions and factor algebraic terms with ease.