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The product of the sum is the sum of the product
Gunitasamuchchayah
The product of the sum of coefficients equals the sum of the product's coefficients. For (x+a)(x+b) = x² + (a+b)x + ab, you can verify a factoring by checking that the sum and product of the constants match the expanded form's middle and last terms.
How It Works
- 1.Given factors (x+a)(x+b), note the constants a and b.
- 2.Compute the sum: a + b. This is the coefficient of x in the expansion.
- 3.Compute the product: a × b. This is the constant term in the expansion.
- 4.The expanded form is x² + (a+b)x + ab.
- 5.Verify by checking: middle coefficient = a+b, constant term = a×b.
Examples
(x+2)(x+3) → x²+5x+6
Step 1 / 5
Expand (x+2)(x+3) mentally using the sutra.
Factor 1x + 2
Factor 2x + 3
Try It Yourself
(x+3)(x+4) → constant term?