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(2x+3)(3x2−2x+5)

3 min read Jun 16, 2024
(2x+3)(3x2−2x+5)

Expanding the Expression (2x+3)(3x²−2x+5)

This article will guide you through the process of expanding the expression (2x+3)(3x²−2x+5). This involves multiplying two polynomials, which can be done using the distributive property or the FOIL method.

Using the Distributive Property

The distributive property states that for any numbers a, b, and c: a(b+c) = ab + ac. We can apply this property to expand our expression:

  1. Distribute the first term (2x) from the first polynomial: (2x)(3x²−2x+5) = 6x³ - 4x² + 10x

  2. Distribute the second term (3) from the first polynomial: (3)(3x²−2x+5) = 9x² - 6x + 15

  3. Combine the results: 6x³ - 4x² + 10x + 9x² - 6x + 15

  4. Simplify by combining like terms: 6x³ + 5x² + 4x + 15

Using the FOIL Method

The FOIL method is a mnemonic device that helps remember the steps for multiplying two binomials. FOIL stands for:

  • First: Multiply the first terms of each binomial.
  • Outer: Multiply the outer terms of the binomials.
  • Inner: Multiply the inner terms of the binomials.
  • Last: Multiply the last terms of each binomials.

Applying FOIL to our expression:

  1. First: (2x)(3x²) = 6x³

  2. Outer: (2x)(5) = 10x

  3. Inner: (3)(-2x) = -6x

  4. Last: (3)(5) = 15

  5. Combine all terms: 6x³ + 10x - 6x + 15

  6. Simplify by combining like terms: 6x³ + 5x² + 4x + 15

Conclusion

Both the distributive property and the FOIL method lead to the same expanded form of the expression (2x+3)(3x²−2x+5): 6x³ + 5x² + 4x + 15. Choose whichever method you find easier to remember and apply.

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