%2B(8x%5E2-5x%2B1)-(3x-4)(7x%2B2).jpeg "(6x^2+2x-9)+(8x^2-5x+1)-(3x-4)(7x+2)")
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.