Expand the Expression: (x-3)(x-6) Using the Distributive Property

Q: What does FOIL stand for and why do I need it?

FOIL stands for First, Outer, Inner, Last. It helps you remember to multiply all four combinations of terms systematically, so you don't miss any!

Q: Why do I get a positive 18 when multiplying two negative numbers?

When you multiply two negative numbers, the result is always positive! $ (-3) \times (-6) = +18 $ because negative times negative equals positive.

Q: How do I combine -6x and -3x correctly?

These are like terms because they both have the variable x. Simply add the coefficients: $ -6 + (-3) = -9 $, so $ -6x - 3x = -9x $.

Q: Can I use this method for any two binomials?

Yes! The FOIL method works for multiplying any two binomials, whether they have addition or subtraction signs. Just be careful with your positive and negative signs.

Q: How can I check if my expanded form is correct?

Pick any number for x (like x = 1) and substitute it into both the original $ (x-3)(x-6) $ and your answer $ x^2-9x+18 $. If you get the same result, you're correct!

Binomial Multiplication with FOIL Method

Resolve -

$(x-3)(x-6)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Open parentheses properly, multiply each factor by each factor

00:26 Calculate the products

00:43 Collect like terms

00:50 Collect like terms

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Resolve -

$(x-3)(x-6)=$

Step-by-step solution

To solve this problem, we will expand the expression $(x-3)(x-6)$ using the distributive property, which involves the following steps:

Step 1: Multiply the first terms of each binomial
$(x)(x) = x^2$
Step 2: Multiply the outer terms of the binomials
$(x)(-6) = -6x$
Step 3: Multiply the inner terms of the binomials
$(-3)(x) = -3x$
Step 4: Multiply the last terms of each binomial
$(-3)(-6) = 18$
Step 5: Combine all the products
$x^2 - 6x - 3x + 18$
Step 6: Combine like terms
$-6x - 3x = -9x$ , so we have
$x^2 - 9x + 18$

Therefore, the expanded form of $(x-3)(x-6)$ is $\boxed{x^2 - 9x + 18}$ .

Therefore, the solution to the problem is $x^2 - 9x + 18$ . This corresponds to choice 1.

Final Answer

$x^2-9x+18$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiply systematically
Technique: $(x)(-6) + (-3)(x) = -6x - 3x = -9x$
Check: Substitute x=3: $(3-3)(3-6) = 0(-3) = 0$ and $9-27+18 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying terms
Don't add the binomials like (x-3) + (x-6) = 2x-9! This completely ignores the multiplication symbol and gives a linear expression instead of quadratic. Always multiply each term in the first binomial by each term in the second binomial using FOIL.

Practice Quiz

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

FAQ

Everything you need to know about this question

What does FOIL stand for and why do I need it?

FOIL stands for First, Outer, Inner, Last. It helps you remember to multiply all four combinations of terms systematically, so you don't miss any!

Why do I get a positive 18 when multiplying two negative numbers?

When you multiply two negative numbers, the result is always positive! $(-3) \times (-6) = +18$ because negative times negative equals positive.

How do I combine -6x and -3x correctly?

These are like terms because they both have the variable x. Simply add the coefficients: $-6 + (-3) = -9$ , so $-6x - 3x = -9x$ .

Can I use this method for any two binomials?

Yes! The FOIL method works for multiplying any two binomials, whether they have addition or subtraction signs. Just be careful with your positive and negative signs.

How can I check if my expanded form is correct?

Pick any number for x (like x = 1) and substitute it into both the original $(x-3)(x-6)$ and your answer $x^2-9x+18$ . If you get the same result, you're correct!

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