Expand the Binomial Product: (x+2)(x-4) Step-by-Step

Q: What does FOIL stand for and why is it helpful?

FOIL stands for First, Outer, Inner, Last - the four multiplication steps needed to expand two binomials. It's helpful because it gives you a systematic way to make sure you don't miss any terms!

Q: What if I mess up the signs during multiplication?

Remember the sign rules: positive × negative = negative and negative × negative = positive. In (x+2)(x-4), when you multiply +2 by -4, you get -8, not +8!

Binomial Expansion with FOIL Method

Solve the following problem:

$(x+2)(x-4)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Open parentheses properly, multiply each factor by each factor

00:21 Calculate the products

00:27 Collect like terms

00:33 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:

$(x+2)(x-4)=$

Step-by-step solution

In order to solve the given problem, we will use the FOIL method. FOIL stands for First, Outer, Inner, Last. This helps us to systematically expand the product of the two binomials:

Step 1: Multiply the First terms.

The first terms of each binomial are $x$ and $x$ . Multiply these together to obtain $x \times x = x^2$ .

Step 2: Multiply the Outer terms.

The outer terms are $x$ and $-4$ . Multiply these. together to obtain $x \times -4 = -4x$ .

Step 3: Multiply the Inner terms.

The inner terms are $2$ and $x$ . Multiply these together to obtain $2 \times x = 2x$ .

Step 4: Multiply the Last terms.

The last terms are $2$ and $-4$ . Multiply these together to obtain $2 \times -4 = -8$ .

Proceed to combine all these results together:

$x^2 - 4x + 2x - 8$

Finally, combine like terms:

Combine $-4x$ and $2x$ to obtain $-2x$ .

The expanded form of the expression is therefore:

$x^2 - 2x - 8$

Thus, the solution to the problem is $x^2 - 2x - 8$ , which corresponds to choice 1.

Final Answer

$x^2-2x-8$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiplied systematically
Technique: $x \times x = x^2$ , then $x \times (-4) = -4x$ , then $2 \times x = 2x$ , then $2 \times (-4) = -8$
Check: Combine like terms $-4x + 2x = -2x$ to get final answer $x^2 - 2x - 8$ ✓

Common Mistakes

Avoid these frequent errors

Incorrect sign handling when combining like terms
Don't combine -4x + 2x to get +2x = wrong final answer x² + 2x - 8! This happens when you forget that -4x means negative four x. Always carefully track signs: -4x + 2x = -2x.

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 is it helpful?

FOIL stands for First, Outer, Inner, Last - the four multiplication steps needed to expand two binomials. It's helpful because it gives you a systematic way to make sure you don't miss any terms!

How do I remember which terms are 'outer' and 'inner'?

Think of the binomials written side by side: (x+2)(x-4). The outer terms are the ones on the outside edges (x and -4), while the inner terms are the ones in the middle (2 and x).

Why do I get four terms first, then only three at the end?

When you use FOIL, you get four separate products initially. But some of these terms are like terms (same variable and power), so you combine them. In this problem, -4x and +2x combine to make -2x.

What if I mess up the signs during multiplication?

Remember the sign rules: positive × negative = negative and negative × negative = positive. In (x+2)(x-4), when you multiply +2 by -4, you get -8, not +8!

Can I check my answer by plugging in a number for x?

Yes! Pick any number for x (like x = 1) and substitute it into both the original expression (x+2)(x-4) and your answer x²-2x-8. If you get the same result, you're correct!

Do I always end up with a quadratic expression?

When multiplying two binomials with x terms, yes! You'll always get an x² term (from multiplying the x's), an x term (from the outer and inner products), and a constant term (from multiplying the numbers).

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