To expand the expression $(−2x+7)(x^2 + 2x−4)$, we use the distributive property (also known as the FOIL method for binomials). Here's the step-by-step process:

Step 1: Distribute $-2x$ to each term in the second polynomial:

$-2x(x^2) + (-2x)(2x) + (-2x)(-4)$ This gives: $-2x^3 - 4x^2 + 8x$

Step 2: Distribute $7$ to each term in the second polynomial:

$7(x^2) + 7(2x) + 7(-4)$ This gives: $7x^2 + 14x - 28$

Step 3: Combine all the terms:

$(-2x^3 - 4x^2 + 8x) + (7x^2 + 14x - 28)$

Step 4: Simplify by combining like terms:

$-2x^3 + (-4x^2 + 7x^2) + (8x + 14x) - 28$ This simplifies to: $-2x^3 + 3x^2 + 22x - 28$

Final Answer:

The expanded polynomial in standard form is: $-2x^3 + 3x^2 + 22x - 28$

Would you like further details or have any questions?

5 Related Questions:

1. How do you factor a cubic polynomial like $-2x^3 + 3x^2 + 22x - 28$?
2. How do you use the distributive property for higher-degree polynomials?
3. What is the importance of standard form in polynomial equations?
4. Can you explain how to find the roots of a cubic polynomial?
5. How would you graph the polynomial $-2x^3 + 3x^2 + 22x - 28$?

Tip:

When expanding polynomials, always combine like terms carefully to ensure accuracy in your final result.