Expand the Binomial Expression: (x-6)(x+2) Step by Step

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

FOIL stands for First, Outer, Inner, Last - the order to multiply terms in binomials. It's a systematic method that ensures you don't miss any terms when expanding $ (x-6)(x+2) $.

Q: How can I check if my expansion is correct?

Try factoring your answer back! If $ x^2 - 4x - 12 $ factors to $ (x-6)(x+2) $, you got it right. You can also substitute a test value like $ x = 1 $ into both expressions.

Q: What if I have trouble with the signs?

Be extra careful with negatives! When you see $ (x-6) $, treat it as $ (x + (-6)) $. This makes the Inner multiplication clearer: $ (-6) \times x = -6x $.

Binomial Multiplication with FOIL Method

$(x-6)(x+2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:04 Open the brackets properly, multiply each factor by each factor

00:18 Calculate the multiplications

00:26 Collect like terms

00:31 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

$(x-6)(x+2)=$

Step-by-step solution

To solve this problem, we need to multiply the binomials $(x-6)$ and $(x+2)$ using the distributive property (FOIL method):

First: Multiply the first terms: $x \cdot x = x^2$
Outer: Multiply the outer terms: $x \cdot 2 = 2x$
Inner: Multiply the inner terms: $-6 \cdot x = -6x$
Last: Multiply the last terms: $-6 \cdot 2 = -12$

Now, we have the terms: $x^2$ , $2x$ , $-6x$ , and $-12$ .
We combine the linear terms:

$x^2 + 2x - 6x - 12 = x^2 - 4x - 12$

This is the expanded form of the quadratic expression in standard form.
Therefore, the solution to the problem is $x^2 - 4x - 12$ .

Final Answer

$x^2-4x-12$

Key Points to Remember

Essential concepts to master this topic

FOIL Rule: First, Outer, Inner, Last terms multiplied systematically
Technique: Combine like terms: $2x + (-6x) = -4x$
Check: Expand $x^2 - 4x - 12$ back to $(x-6)(x+2)$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms after FOIL
Don't leave your answer as $x^2 + 2x - 6x - 12$ = incomplete expansion! This misses the crucial step of simplification. Always combine the middle terms: $2x - 6x = -4x$ to get the final form.

Practice Quiz

Test your knowledge with interactive questions

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

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 - the order to multiply terms in binomials. It's a systematic method that ensures you don't miss any terms when expanding $(x-6)(x+2)$ .

Why do I get a negative sign in my middle term?

The middle term comes from adding the Outer and Inner products: $2x + (-6x) = -4x$ . Since $-6x$ is larger in absolute value than $2x$ , the result is negative.

How can I check if my expansion is correct?

Try factoring your answer back! If $x^2 - 4x - 12$ factors to $(x-6)(x+2)$ , you got it right. You can also substitute a test value like $x = 1$ into both expressions.

What if I have trouble with the signs?

Be extra careful with negatives! When you see $(x-6)$ , treat it as $(x + (-6))$ . This makes the Inner multiplication clearer: $(-6) \times x = -6x$ .

Do I always get a quadratic when multiplying two binomials?

Yes! When you multiply two linear binomials, you always get a quadratic expression (degree 2). The highest power will be $x^2$ from multiplying the First terms together.

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