Vedic maths · trick 29 of 36 · free

Algebra: longer expressions — Vedic maths trick

Trick 20 multiplied two brackets with x. The same columns work with an x² term, and with two letters x and y.

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The trick

Urdhva Tiryagbhyam — “vertically and crosswise”

(ax² + bx + c)(dx + e): x³ = a×d; x² = a×e + b×d; x = b×e + c×d; number = c×e.
(ax + by)(cx + dy): x² = a×c; xy = a×d + b×c; y² = b×d.
Keep the signs; leave out a term whose total is 0. Type x³ as x^3.

Use it for: Class 8–10 algebra: multiplying polynomials and expanding expressions with two variables.

Worked example: (x² + 2x + 3)(x + 4) = x³ + 6x² + 11x + 12

x³: 1 × 1 = 1.
x²: 1 × 4 + 2 × 1 = 6.
x: 2 × 4 + 3 × 1 = 11. Number: 3 × 4 = 12.
Answer: x³ + 6x² + 11x + 12.

Check: Put x = 1: (6)(5) = 30 and 1 + 6 + 11 + 12 = 30 ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

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🏁 Trick 29 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Multiplying Polynomials Worksheet

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