(4m+9)(-4m^2+m+3)

2 min read Jun 16, 2024

Multiplying Polynomials: (4m + 9)(-4m² + m + 3)

This article will guide you through the steps of multiplying the two polynomials (4m + 9) and (-4m² + m + 3).

Understanding the Process

Multiplying polynomials involves distributing each term of one polynomial to every term of the other polynomial. This can be visualized using the FOIL method (First, Outer, Inner, Last) for binomials or the distributive property for any polynomial.

Applying the Distributive Property

Distribute the first term of the first polynomial:
- 4m * (-4m²) = -16m³
- 4m * m = 4m²
- 4m * 3 = 12m
Distribute the second term of the first polynomial:
- 9 * (-4m²) = -36m²
- 9 * m = 9m
- 9 * 3 = 27

Combining Like Terms

Now that we have expanded the product, we can combine the like terms to simplify the expression:

-16m³ + 4m² + 12m - 36m² + 9m + 27

Combining like terms:

-16m³ - 32m² + 21m + 27

Conclusion

Therefore, the product of (4m + 9) and (-4m² + m + 3) is -16m³ - 32m² + 21m + 27.

This process demonstrates how to multiply polynomials using the distributive property and simplify the resulting expression by combining like terms.