Q3 of 59 Page 38

Find the expression for the product (x + a)(x + b)(x + c) using the identity (x + a)(x + b) = x2 + (a + b)x + ab

first we will expand (x + a)(x + b)

Using the identity


(x+a) (x+b) = x2 + (a+b) x + ab


= x2 + (a+b) x + ab


Now multiplying the expansion with (x+c)


(x2 + (a+b) x + ab) (x+c)


By using the distributive law


x(x2 + (a+b) x + ab) + c(x2 + (a+b) x + ab)


= x3 +(a+b)x2 +abx + cx2 +(a+b) cx +abc


Arranging the like terms


= x3 + (a+ b+ c)x2 + abx + acx + bcx +abc


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


More from this chapter

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1

Find the product:

(i) (a + 3)(a + 5)


(ii) (3t + 1)(3t + 4)


(iii) (a – 8)(a + 2)


(iv) (a – 6)(a – 2)

 2

Evaluate using suitable identities:

(i) 53 × 55 (ii) 102 × 106


(iii) 34 × 36 (iv) 103 × 96

 4

Using the identity (a +b)2 = a2 + 2ab + b2, simplify the following:

(i) (a + 6)2 (ii) (3x + 2y)2


(iii) (2p + 3q)2 (iv) (x2 + 5)2

 5

Evaluate using the identity (a + b)2 = a2 + 2ab + b2

(i) (34)2 (ii) (10.2)2


(iii) (53)2 (iv) (41)2