InterviewSolution
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InterviewSolution
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Find the expression for the product (x+a) (x+b) (x+c) using the identity (x + a)(x + b) = x2 + (a + b)x + ab |
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Answer» (x + a) (x + b) (x + c) Consider (x + a)(x + b) = x2 + (a + b)x + ab = x2 + ax + bx + ab (x + a)(x + b)(x + c) = (x2 + ax + bx + ab)(x + c) = x(x2 + ax + bx+ ab) + c (x2 + ax + bx + ab) = x3 + ax2 + bx2 + abx + cx2 + cax +cbx + abc = x3 + ax2 + bx2+ cx2 + abx + cax +cbx + abc [by rearranging] = x3 + x2(a + b + c) + x(ab + ca +bc) + abc ∴ (x + a)(x + b)(x + c) = x3 +x2 (a + b + c) + x(ab + bc + ca) + abc |
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