Q3 of 59 Page 7

Using algebraic identities find the coefficients of x2 term, x term and constant term.

(x + 7)(x + 3)(x + 9)

Here we have to use the identity


(x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc


∴ (x + 7)(x + 3)(x + 9)


= x3 + (7 + 3 + 9)x2 + (7 × 3 + 3 × 9 + 9 × 7)x + 7 × 3 × 9


= x3 + 19x2 + (21 + 27 + 63)x + 189


= x3 + 19x2 + 111x + 189


Coefficient of


x2 = 19


x = 111


Constant term = 189


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