Sum

Using algebraic identity, find the coefficients of x^{2}, x and constant term without actual expansion

(x + 5)(x + 6)(x + 7)

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#### Solution

(x + 5)(x + 6)(x + 7)

(x + a)(x + b)(x + c) ≡ x^{3} + (a + b + c)x^{2} + (ab + bc + ca)x + abc

Co-efficient of x^{2} = a + b + c = 5 + 6 + 7 = 18

Co-efficient of x^{2} = ab + bc + ca

= (5 × 6) + (6 × 7) + (7 × 5)

= 30 + 42 + 35

= 107

Constant term = abc = 5 × 6 × 7

Co-efficient of constant term = 210

Concept: Concept of Identity

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