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(x+1)(x+3) In Standard Form

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

Expanding (x + 1)(x + 3) into Standard Form

The expression (x + 1)(x + 3) is in factored form. To write it in standard form, we need to expand it. Here's how:

Using the FOIL Method

The FOIL method is a mnemonic for remembering how to multiply two binomials:

  • 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 to our expression:

  • F: x * x = x²
  • O: x * 3 = 3x
  • I: 1 * x = x
  • L: 1 * 3 = 3

Now, we add all the terms together: x² + 3x + x + 3

Combining like terms, we get:

x² + 4x + 3

This is the standard form of the expression (x + 1)(x + 3).

Using the Distributive Property

We can also use the distributive property to expand the expression:

(x + 1)(x + 3) = x(x + 3) + 1(x + 3)

Distributing further:

= x² + 3x + x + 3

Combining like terms, we get:

x² + 4x + 3

This confirms that both methods lead to the same answer.

Conclusion

The standard form of the expression (x + 1)(x + 3) is x² + 4x + 3. This form is useful for various algebraic operations, like solving equations, finding the roots of the expression, or graphing the function represented by the expression.

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