Expand the Expression: (3x-1)(x+2) Using Distribution Method

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

FOIL stands for First, Outer, Inner, Last - it helps you remember to multiply all four combinations when expanding two binomials. Use it whenever you see expressions like (a+b)(c+d).

Q: Why do I get four terms before combining like terms?

When you distribute properly, you create four separate products. In $ (3x-1)(x+2) $, you get: 3x², +6x, -x, and -2. Then you combine the like terms 6x and -x to get 5x.

Q: How do I know which terms are like terms?

Like terms have the same variable and exponent. In this problem, 6x and -x are like terms because they both have x¹. The terms 3x² and -2 are unlike any others, so they stay as is.

Q: What if I make a sign error during distribution?

Sign errors are common! When distributing negative terms like (-1), remember that (-1) × (+2) = -2 and (-1) × (+x) = -x. Always double-check your signs in each step.

Binomial Multiplication with Distribution Method

Solve the exercise:

$(3x-1)(x+2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this problem together.

00:11 First, open the parentheses and multiply each part carefully.

00:33 Now, let's calculate these products step by step.

01:01 Remember, a positive times a negative is always negative.

01:12 Next, collect like terms together.

01:17 Great job! That's how we find the solution to this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the exercise:

$(3x-1)(x+2)=$

Step-by-step solution

To solve this problem, we'll apply the distributive property to expand the expression $(3x-1)(x+2)$ . Below are the steps:

Step 1: Distribute each term in the first binomial to each term in the second binomial:

$3x(x) + 3x(2) + (-1)(x) + (-1)(2)$

Step 2: Calculate each term:

$3x^2 + 6x - x - 2$

Step 3: Combine like terms:

$3x^2 + (6x - x) - 2 = 3x^2 + 5x - 2$

Thus, the expanded expression is $3x^2 + 5x - 2$ .

The correct answer choice is $3x^2 + 5x - 2$ , corresponding to choice id="4".

Final Answer

$3x^2+5x-2$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Multiply each term in first binomial by every term in second binomial
Technique: Use FOIL: First $3x \cdot x = 3x^2$ , Outer $3x \cdot 2 = 6x$ , Inner $(-1) \cdot x = -x$ , Last $(-1) \cdot 2 = -2$
Check: Combine like terms: $3x^2 + 6x - x - 2 = 3x^2 + 5x - 2$ ✓

Common Mistakes

Avoid these frequent errors

Only multiplying first terms and last terms
Don't just multiply 3x × x = 3x² and (-1) × 2 = -2 to get 3x² - 2! This skips the middle terms and gives wrong answers. Always multiply every term in the first binomial by every term in the second binomial using FOIL or distribution.

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 when do I use it?

FOIL stands for First, Outer, Inner, Last - it helps you remember to multiply all four combinations when expanding two binomials. Use it whenever you see expressions like (a+b)(c+d).

Why do I get four terms before combining like terms?

When you distribute properly, you create four separate products. In $(3x-1)(x+2)$ , you get: 3x², +6x, -x, and -2. Then you combine the like terms 6x and -x to get 5x.

How do I know which terms are like terms?

Like terms have the same variable and exponent. In this problem, 6x and -x are like terms because they both have x¹. The terms 3x² and -2 are unlike any others, so they stay as is.

What if I make a sign error during distribution?

Sign errors are common! When distributing negative terms like (-1), remember that (-1) × (+2) = -2 and (-1) × (+x) = -x. Always double-check your signs in each step.

Can I check my answer by substituting a number for x?

Yes! Pick any number for x (like x = 1) and verify that both $(3x-1)(x+2)$ and $3x^2+5x-2$ give the same result. If x = 1: (2)(3) = 6 and 3+5-2 = 6 ✓

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