Question

Deduce the Algebraic identity for (x + a) (x + b) (x + c) by using the product

Answer 1

this is the solution to the problem

Answer 2

Solution:

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We know the algebraic identity:

(x+a)(x+b)= x²+(a+b)+ab

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Now ,

(x+a)(x+b)(x+c)

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

= [x²+(a+b)x+ab](x+c)

= [x²+(a+b)x+ab]x+[x²+(a+b)x+ab]c

= x³+(a+b)x²+abx + x²c+(a+b)cx+abc

= x³+(a+b+c)x²+(ab+bc+ca)x+abc

Therefore,

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(x+a)(x+b)(x+c)

= x³+(a+b+c)x²+(ab+bc+ca)x+abc

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