(x+5)(x-7) Answer

Jasonbradley

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Jun 17, 2024

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Expanding the Expression (x+5)(x-7)

In mathematics, expanding an expression means to simplify it by multiplying out any brackets. Here's how to expand the expression (x+5)(x-7):

Using the FOIL Method

The FOIL method is a common technique for expanding expressions like this. FOIL stands for:

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

Let's apply this to our expression:

1. First: x * x = x²
2. Outer: x * -7 = -7x
3. Inner: 5 * x = 5x
4. Last: 5 * -7 = -35

Now, combine the terms:

x² - 7x + 5x - 35

Finally, simplify by combining like terms:

x² - 2x - 35

Alternative Approach: Distributive Property

You can also use the distributive property to expand the expression. The distributive property states that a(b + c) = ab + ac.

Here's how it applies to our problem:

1. Distribute the first term (x) from the first bracket to both terms in the second bracket: x(x-7) = x² - 7x

2. Distribute the second term (5) from the first bracket to both terms in the second bracket: 5(x-7) = 5x - 35

3. Combine the results: x² - 7x + 5x - 35

4. Simplify: x² - 2x - 35

Both methods lead to the same answer: x² - 2x - 35.