## Simplifying the Expression: (6x^2+2x-9)+(8x^2-5x+1)-(3x-4)(7x+2)

This article will guide you through simplifying the given algebraic expression.

### Step 1: Expanding the Product

The first step is to expand the product of the two binomials using the FOIL method (First, Outer, Inner, Last).

(3x-4)(7x+2) = (3x * 7x) + (3x * 2) + (-4 * 7x) + (-4 * 2)

= 21x^2 + 6x - 28x - 8

= 21x^2 - 22x - 8

### Step 2: Combining Like Terms

Now that the product has been expanded, we can combine the like terms in the entire expression.

(6x^2 + 2x - 9) + (8x^2 - 5x + 1) - (21x^2 - 22x - 8)

= **6x^2** + 2x - 9 + **8x^2** - 5x + 1 - **21x^2** + 22x + 8

### Step 3: Simplifying the Expression

Combining the coefficients of the like terms:

= (6 + 8 - 21)x^2 + (2 - 5 + 22)x + (-9 + 1 + 8)

= **-7x^2 + 19x**

### Conclusion

Therefore, the simplified form of the given expression (6x^2+2x-9)+(8x^2-5x+1)-(3x-4)(7x+2) is **-7x^2 + 19x**.