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

2 min read Jun 17, 2024
(x+5)(x^2-3x) Foil Method

Using the FOIL Method to Expand (x+5)(x^2 - 3x)

The FOIL method is a handy acronym that helps us remember the steps for multiplying two binomials. It 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 binomial.

Let's apply this method to expand the expression (x+5)(x^2 - 3x):

Step 1: First

  • Multiply the first terms of each binomial: x * x^2 = x^3

Step 2: Outer

  • Multiply the outer terms of the binomials: x * -3x = -3x^2

Step 3: Inner

  • Multiply the inner terms of the binomials: 5 * x^2 = 5x^2

Step 4: Last

  • Multiply the last terms of the binomials: 5 * -3x = -15x

Step 5: Combine like terms

Now we have: x^3 - 3x^2 + 5x^2 - 15x

Combining like terms gives us: x^3 + 2x^2 - 15x

Therefore, the expanded form of (x+5)(x^2 - 3x) is x^3 + 2x^2 - 15x.

Key Points:

  • The FOIL method is a systematic way to multiply binomials.
  • Remember to combine like terms after applying the FOIL method.
  • This method is a fundamental concept in algebra, and it's essential to understand it for solving various equations and expressions.

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