Expand the Expression: (x+7)(x-9) with Step-by-Step Solution

Q: Why do I need to calculate 3² before using FOIL?

You must follow the order of operations (PEMDAS)! Exponents come before multiplication, so $ 3^2 = 9 $ must be calculated first. This gives you the correct binomial $ (x+7)(x-9) $ to expand.

Q: What does FOIL stand for and how do I use it?

FOIL stands for First, Outer, Inner, Last. Multiply the first terms, then outer terms, then inner terms, then last terms. Finally, combine like terms in your result.

Q: Can I use a different method instead of FOIL?

Yes! You can use the distributive property twice: $ (x+7)(x-9) = x(x-9) + 7(x-9) $. Both methods give the same answer when done correctly.

Q: How can I check if my final answer is correct?

Substitute a simple value like x = 0 into both the original expression and your answer. If $ (0+7)(0-9) = -63 $ and $ 0^2 - 2(0) - 63 = -63 $, your expansion is correct!

Binomial Expansion with Exponent Simplification

Solve the following problem:

$(x+7)(x-3^2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Calculate the power

00:08 Open parentheses properly, multiply each factor by each factor

00:23 Calculate the products

00:35 Combine factors

00:40 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$(x+7)(x-3^2)=$

Step-by-step solution

In order to solve the following expression $(x+7)(x-3^2)$ , we need to follow these steps:

Step 1: Simplify $3^2$ to obtain 9. Thus, rewrite the expression as $(x+7)(x-9)$ .
Step 2: Apply the FOIL method to expand the expression:

Using the FOIL method, the expansion is as follows:

First: $x \times x = x^2$
Outer: $x \times -9 = -9x$
Inner: $7 \times x = 7x$
Last: $7 \times -9 = -63$

Combine these results together:

$x^2 - 9x + 7x - 63$

Step 3: Combine like terms:

The terms $-9x$ and $7x$ can be combined to yield the following $-2x$ .

Thus, the expanded and simplified expression is:

$x^2 - 2x - 63$

Therefore, the final solution is:

$x^2 - 2x - 63$

Final Answer

$x^2-2x-63$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Simplify exponents before applying distribution methods
FOIL Method: First $x \cdot x = x^2$ , Outer $x \cdot (-9) = -9x$ , Inner $7 \cdot x = 7x$ , Last $7 \cdot (-9) = -63$
Verification: Check by substituting x=0: $0^2 - 2(0) - 63 = -63$ and $(0+7)(0-9) = -63$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the exponent first
Don't expand $(x+7)(x-3^2)$ directly without calculating $3^2 = 9$ first = wrong binomial factors! This leads to incorrect FOIL results and wrong final answer. Always simplify all exponents before applying any distribution or expansion methods.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

Why do I need to calculate 3² before using FOIL?

You must follow the order of operations (PEMDAS)! Exponents come before multiplication, so $3^2 = 9$ must be calculated first. This gives you the correct binomial $(x+7)(x-9)$ to expand.

What does FOIL stand for and how do I use it?

FOIL stands for First, Outer, Inner, Last. Multiply the first terms, then outer terms, then inner terms, then last terms. Finally, combine like terms in your result.

How do I combine -9x and +7x correctly?

Since both terms have the same variable x, you can add their coefficients: $-9x + 7x = (-9 + 7)x = -2x$ . Remember that adding a positive to a negative gives you the difference.

Can I use a different method instead of FOIL?

Yes! You can use the distributive property twice: $(x+7)(x-9) = x(x-9) + 7(x-9)$ . Both methods give the same answer when done correctly.

How can I check if my final answer is correct?

Substitute a simple value like x = 0 into both the original expression and your answer. If $(0+7)(0-9) = -63$ and $0^2 - 2(0) - 63 = -63$ , your expansion is correct!

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