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(2x+1)(x^3-4x+5)

2 min read Jun 16, 2024
(2x+1)(x^3-4x+5)

Expanding the Expression (2x+1)(x^3-4x+5)

This article will guide you through expanding the expression (2x+1)(x^3-4x+5). This involves applying the distributive property, also known as the FOIL method, to multiply the two polynomials.

Understanding the Distributive Property

The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

This means we multiply each term inside the parentheses by the factor outside.

Expanding the Expression

  1. Multiply the first term of the first polynomial (2x) by each term in the second polynomial:

    2x * x^3 = 2x^4 2x * -4x = -8x^2 2x * 5 = 10x

  2. Multiply the second term of the first polynomial (1) by each term in the second polynomial:

    1 * x^3 = x^3 1 * -4x = -4x 1 * 5 = 5

  3. Combine the results from steps 1 and 2:

    (2x+1)(x^3-4x+5) = 2x^4 - 8x^2 + 10x + x^3 - 4x + 5

  4. Combine like terms:

    (2x+1)(x^3-4x+5) = 2x^4 + x^3 - 8x^2 + 6x + 5

Conclusion

Therefore, the expanded form of the expression (2x+1)(x^3-4x+5) is 2x^4 + x^3 - 8x^2 + 6x + 5. This process demonstrates the power of the distributive property in simplifying and manipulating algebraic expressions.

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