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

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

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

This article will demonstrate how to expand the expression (x+5)(2x^2-3x+3) using the distributive property, also known as the FOIL method.

Understanding the Distributive Property

The distributive property states that: a(b+c) = ab + ac.

We can apply this property to expand our expression. Think of (x+5) as a single term that needs to be multiplied by each term within the second set of parentheses.

Step-by-Step Solution

  1. Multiply (x+5) by 2x^2:

    • x * 2x^2 = 2x^3
    • 5 * 2x^2 = 10x^2

  2. Multiply (x+5) by -3x:

    • x * -3x = -3x^2
    • 5 * -3x = -15x

  3. Multiply (x+5) by 3:

    • x * 3 = 3x
    • 5 * 3 = 15

  4. Combine all the terms:

    • 2x^3 + 10x^2 - 3x^2 - 15x + 3x + 15

  5. Simplify by combining like terms:

    • 2x^3 + 7x^2 - 12x + 15

Conclusion

By applying the distributive property, we have successfully expanded the expression (x+5)(2x^2-3x+3) into the simplified polynomial 2x^3 + 7x^2 - 12x + 15.

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