Q10 of 157 Page 22

Deduce the Algebraic identity for (x + a) (x + b) (x + c) by using the product formula. [Hint: (x + a) (x + b)(x + c) = (x + a) [(x + b)(x + c)]]

Given (x + a)(x + b)(x + c) = (x + a)[(x + b)(x + c)]


⇒ (x + a)(x + b)(x + c) = (x + a)[x (x + c) + b(x + c)]


⇒ (x + a)(x + b)(x + c) = (x + a)[x2 + cx + bx + bc]


⇒ (x + a)(x + b)(x + c) = (x + a)[x2 + x(c + b) + bc]


⇒ (x + a)(x + b)(x + c) = x[x2 + x(c + b) + bc] + a[x2 + x(c + b) + bc]


⇒ (x + a)(x + b)(x + c) = x3 + x2(c + b) + xbc + ax2 + xa(c + b) + abc


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


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