Algebraic Identities Questions with Solutions

A handful of fixed identities let you find a²+b² or ab without ever solving for a and b individually — and the same identities turn an awkward multiplication like 97×103 into subtraction. Here’s the concept, four fully worked examples, and a few to try yourself.

The concept, quickly

• The two core identities: (a+b)² = a² + 2ab + b², and (a−b)² = a² − 2ab + b². Rearranged, each one connects a²+b² to (a+b)² or (a−b)² and ab — given any two of the three, find the third.
• Difference of squares: a² − b² = (a+b)(a−b) — this is the shortcut behind multiplying two numbers that are equally far from a round number, like 97×103 = (100−3)(100+3).
• When a question gives a+b (or a−b) and ab, it’s testing whether you know a²+b² = (a+b)² − 2ab (or (a−b)² + 2ab) — don’t try to find a and b individually first.
• These identities work in both directions: use them to expand an expression, or to go from a²+b² and a+b (or a−b) back to find ab.

Worked examples

Try these yourself

Identify which identity connects the given values, then check against the answer.

Where this comes up

Algebraic Identities is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and the difference-of-squares shortcut speeds up Simplification and Approximation questions too.

Practice more Algebraic Identities questions

This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Algebraic Identities (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.