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(x+1)(x+3)

2 min read Jun 16, 2024
(x+1)(x+3)

Expanding (x+1)(x+3)

This expression is a product of two binomials, and we can expand it using the distributive property or the FOIL method.

Distributive Property

The distributive property states that a(b+c) = ab + ac. We can apply this to our problem:

  1. Distribute (x+1) over (x+3): (x+1)(x+3) = (x+1) * x + (x+1) * 3

  2. Distribute again: x * x + 1 * x + x * 3 + 1 * 3

  3. Simplify: x² + x + 3x + 3

  4. Combine like terms: x² + 4x + 3

FOIL Method

FOIL stands for First, Outer, Inner, Last, which helps us remember the order of multiplication:

  1. First: Multiply the first terms of each binomial: x * x = x²
  2. Outer: Multiply the outer terms of the binomials: x * 3 = 3x
  3. Inner: Multiply the inner terms of the binomials: 1 * x = x
  4. Last: Multiply the last terms of the binomials: 1 * 3 = 3

This gives us the same result as before: x² + 3x + x + 3 = x² + 4x + 3

Conclusion

Therefore, the expanded form of (x+1)(x+3) is x² + 4x + 3. This is a quadratic expression, meaning it has a highest power of 2.

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