Expand (5x-2)(3+x): Solving Binomial Expression Multiplication

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

FOIL stands for First, Outer, Inner, Last - the order you multiply terms in two binomials. It helps you remember to multiply every term in the first binomial with every term in the second, so you don't miss any products!

Q: Why do I get x² in my answer when the original problem only had x?

When you multiply $ 5x \times x $, you get $ 5x^2 $ because x × x = x². This is normal! Multiplying binomials often creates quadratic expressions (with x² terms).

Q: How do I know which terms to combine at the end?

Only combine like terms - terms with the same variable and exponent. In this problem, $ 15x $ and $ -2x $ are both 'x terms' so they combine to $ 13x $.

Q: Can I multiply binomials in a different order?

Yes! You can multiply $ (3+x)(5x-2) $ instead and get the same answer. The commutative property means order doesn't matter for multiplication.

Q: What if I make an arithmetic error while combining terms?

Always double-check your arithmetic! For $ 15x - 2x $, think: 15 - 2 = 13, so the answer is $ 13x $. Write each step clearly to avoid simple mistakes.

Binomial Multiplication with FOIL Method

Solve the exercise:

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

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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 term by each term

00:23 Calculate the products

00:51 Positive times negative always equals negative

01:00 Arrange the expression, group terms

01:09 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 exercise:

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

Step-by-step solution

To solve the problem $(5x-2)(3+x)$ , we will use the distributive property, specifically the FOIL (First, Outer, Inner, Last) method, to expand the expression:

Step 1: Multiply the First terms: $5x \times 3 = 15x$ .
Step 2: Multiply the Outer terms: $5x \times x = 5x^2$ .
Step 3: Multiply the Inner terms: $-2 \times 3 = -6$ .
Step 4: Multiply the Last terms: $-2 \times x = -2x$ .

Now combine all these products together:

$5x^2 + 15x - 2x - 6$

Combine the like terms $15x$ and $-2x$ :

$5x^2 + (15x - 2x) - 6 = 5x^2 + 13x - 6$

Thus, the expanded form of the expression is $5x^2 + 13x - 6$ .

Final Answer

$5x^2+13x-6$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiply systematically
Technique: $5x \times x = 5x^2$ and $15x - 2x = 13x$
Check: Substitute x=1: $5(1)^2 + 13(1) - 6 = 12$ and $(5-2)(3+1) = 12$ ✓

Common Mistakes

Avoid these frequent errors

Missing the x² term when multiplying variables
Don't multiply 5x × x = 5x instead of 5x² = wrong degree polynomial! This happens when students forget that x × x = x², not just x. Always remember that multiplying like variables creates exponents: x × x = x².

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 order you multiply terms in two binomials. It helps you remember to multiply every term in the first binomial with every term in the second, so you don't miss any products!

Why do I get x² in my answer when the original problem only had x?

When you multiply $5x \times x$ , you get $5x^2$ because x × x = x². This is normal! Multiplying binomials often creates quadratic expressions (with x² terms).

How do I know which terms to combine at the end?

Only combine like terms - terms with the same variable and exponent. In this problem, $15x$ and $-2x$ are both 'x terms' so they combine to $13x$ .

Can I multiply binomials in a different order?

Yes! You can multiply $(3+x)(5x-2)$ instead and get the same answer. The commutative property means order doesn't matter for multiplication.

What if I make an arithmetic error while combining terms?

Always double-check your arithmetic! For $15x - 2x$ , think: 15 - 2 = 13, so the answer is $13x$ . Write each step clearly to avoid simple mistakes.

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