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(8x^{2} - 15x) - (x^{2} - 27x) = ax^{2} + bx

If the equation above is true for all values of x, what is the value of b - a ?

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(8x^{2} - 15x) - (x^{2} - 27x) = ax^{2} + bx

8x^{2} - 15x - x^{2} + 27x = ax^{2} + bx

7x^{2} + 12x = ax^{2} + bx

since the equation is true for all values of x, we can compare the coefficient each terms.

Comparing the coefficient of x^{2},

a = 7

Similarly, if we compare the coefficient of x,

b = 12

Thus,

b - a = 12 - 7

= 5

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