If foil ( x - 2) ( 5x + 2) and foil (3x + 5)(x - 2) + (2x - 3)(x - 2) then combine like term would i get the same solution ?

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We can see that x-2 is a common factor x-2. We add the two expression:

( x - 2) ( 5x + 2) and (3x + 5)(x - 2) + (2x - 3)(x - 2) and find the solution

= (x-2)(5x+2+3x+5+2x-3) = 0

(x-2)(10x-4) = 0. We d

**So x-2 = 0 or x=2 is the common solution.**

If FOIL method is used for (x - 2)(5x + 2) the result is 5x^2 + 2x - 10x - 4

=> 5x^2 - 8x - 4 ...(1)

If FOIL method is used for (3x + 5)(x - 2) + (2x - 3)(x - 2) we get

3x^2 - 6x + 5x - 10 + 2x^2 - 4x - 3x + 6

adding the like terms

=> 5x^2 - 8x - 4 ...(2)

(1) and (2) are the same.

**This proves that you will get the same solution for both the expressions.**

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