
Steps  6x^{2} + 13x + 5 = (2x + 1)(3x + 5)  
1.  Write the expression in equated form, with the factors in one side, preferable LHS, and the product on the other, preferably RHS.  In this case, (2x + 1)(3x + 5) = 6x^{2} + 13x + 5 

2.  Find the product of the (Sum of all the coefficients) of the factors.  In this case, LHS = (2 + 1) × (3 + 5) = 3 × 8 = 24 

3.  Find the sum of all the coefficients of the product expression.  In this case, RHS = 6 + 13 + 5 = 24 

4.  These two sums will always be the same. If, not the factors are incorrect and the expression cannot be equated.  In this case, since LHS = RHS, the expression in equated! 
The above expression is not equated because: Coefficients of LHS = (2 + 3)(1  2) = 5 Coefficients of RHS = 2  5  6 = 9 Thus, (2x + 3)(x  2) ≠ 2x^{2}  5x  6 
Coefficients of LHS = (1 + 2)(1 + 3)(1 + 8) = 108 Coefficients of RHS = 1 + 13 + 44 + 48 = 106 Thus, (x + 2)(x + 3)(x + 8) ≠ x^{3} + 13x^{2} + 44x + 48 
Coefficients of LHS = (1 + 1)(1 + 2)(1 + 3) = 24 Coefficients of RHS = 1 + 6 + 11 + 6 = 24 Thus, (x + 1)(x + 2)(x + 3) = x^{3} + 6x^{2} + 11x + 6, is equated. 

For any Quadratic expression: (ax + b)(cx + d) = ac x^{2} + bc x + ad x + bd Considering only the coefficients: ac + bc + ad + bd = a(c + d) + b(c + d) = (a + b)(c + d) Note, that Cubic and BiQuadratic expressions may be proven similarly. 
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