Answer :

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

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

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

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

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