How do you expand (x + 5)(x - 3)?

To expand \((x + 5)(x - 3)\), use the distributive property to get \(x^2 - 3x + 5x - 15\).

When expanding binomials like \((x + 5)(x - 3)\), you can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). This method helps you multiply each term in the first binomial by each term in the second binomial.

First, multiply the first terms in each binomial: \(x \times x = x^2\).

Next, multiply the outer terms: \(x \times -3 = -3x\).

Then, multiply the inner terms: \(5 \times x = 5x\).

Finally, multiply the last terms: \(5 \times -3 = -15\).

Now, combine all these products: \(x^2 - 3x + 5x - 15\).

To simplify, combine the like terms \(-3x\) and \(5x\): \(x^2 + 2x - 15\).

So, the expanded form of \((x + 5)(x - 3)\) is \(x^2 + 2x - 15\). This method ensures you account for every possible product between the terms in the binomials, leading to the correct expanded expression.