(3x-4)(x+7)-1/4x^2 As A Trinomial In Standard Form

2 min read Jun 16, 2024

(3x-4)(x+7)-1/4x^2 As A Trinomial In Standard Form

Expanding and Simplifying the Expression: (3x-4)(x+7) - 1/4x^2

This article will guide you through the process of expanding and simplifying the given expression, (3x-4)(x+7) - 1/4x^2, into a trinomial in standard form.

Step 1: Expanding the Binomials

Firstly, we need to expand the product of the two binomials, (3x-4)(x+7). This is done by using the FOIL method:

First: (3x)(x) = 3x²
Outer: (3x)(7) = 21x
Inner: (-4)(x) = -4x
Last: (-4)(7) = -28

Therefore, (3x-4)(x+7) expands to: 3x² + 21x - 4x - 28

Step 2: Combining Like Terms

Now, we can simplify the expression by combining like terms:

3x² + 21x - 4x - 28 - 1/4x²

This becomes: (3 - 1/4)x² + (21 - 4)x - 28

Step 3: Simplifying the Coefficients

Finally, we can simplify the coefficients:

11/4x² + 17x - 28

Conclusion

The given expression, (3x-4)(x+7) - 1/4x², simplifies to 11/4x² + 17x - 28 when expressed as a trinomial in standard form. This form allows for easier analysis and manipulation of the polynomial.