Convert f(x) = (x-6)(x-2) to Its Standard Quadratic Form

Q: What does FOIL stand for again?

FOIL stands for First, Outside, Inside, Last - the order you multiply terms in two binomials. It's a memory trick to make sure you don't miss any products!

Q: Why is the constant term positive when both numbers are negative?

When you multiply two negative numbers, you get a positive result! So (-6) × (-2) = +12. Remember: negative times negative equals positive.

Q: How do I know which terms are 'like terms' to combine?

Like terms have the same variable and exponent. Here, -2x and -6x are both 'x terms' so they combine: -2x + (-6x) = -8x.

Q: What if I get the wrong sign on the middle term?

Double-check your Outside and Inside steps! For (x-6)(x-2): Outside gives x×(-2) = -2x, Inside gives (-6)×x = -6x. Combined: -2x + (-6x) = -8x.

Expanding Binomials with FOIL Method

Find the standard representation of the following function

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify to the standard representation of the function

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

00:16 Collect like terms

00:23 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

Find the standard representation of the following function

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

Step-by-step solution

To find the standard representation of the quadratic function $f(x) = (x - 6)(x - 2)$ , follow these steps:

Step 1: Apply the FOIL method to expand the expression.
- First: Multiply the first terms: $x \times x = x^2$ .
- Outside: Multiply the outer terms: $x \times (-2) = -2x$ .
- Inside: Multiply the inner terms: $(-6) \times x = -6x$ .
- Last: Multiply the last terms: $(-6) \times (-2) = 12$ .
Step 2: Combine the results from the FOIL method.
- Combine all the expanded terms: $x^2 - 2x - 6x + 12$ .
Step 3: Simplify by combining like terms.
- Combine the $x$ -terms: $-2x - 6x = -8x$ .
- The expanded and simplified form is: $f(x) = x^2 - 8x + 12$ .

By expanding and simplifying the given product, we have converted it to its standard form. Therefore, the standard representation of the function is $f(x) = x^2 - 8x + 12$ .

The correct choice from the provided options is choice 2: $f(x) = x^2 - 8x + 12$ .

Final Answer

$f(x)=x^2-8x+12$

Key Points to Remember

Essential concepts to master this topic

Rule: Use FOIL to multiply binomials systematically
Technique: First (x·x = x²), Outside (x·-2 = -2x), Inside (-6·x = -6x), Last (-6·-2 = 12)
Check: Combine like terms: -2x + (-6x) = -8x gives x² - 8x + 12 ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients instead of multiplying
Don't add -6 and -2 to get -8 as the constant term = x² - 8x - 8! This skips the actual multiplication step. Always multiply the last terms: (-6) × (-2) = +12.

Practice Quiz

Test your knowledge with interactive questions

Create an algebraic expression based on the following parameters:

$$ a=2,b=2,c=2 $$

FAQ

Everything you need to know about this question

What does FOIL stand for again?

FOIL stands for First, Outside, Inside, Last - the order you multiply terms in two binomials. It's a memory trick to make sure you don't miss any products!

Why is the constant term positive when both numbers are negative?

When you multiply two negative numbers, you get a positive result! So (-6) × (-2) = +12. Remember: negative times negative equals positive.

How do I know which terms are 'like terms' to combine?

Like terms have the same variable and exponent. Here, -2x and -6x are both 'x terms' so they combine: -2x + (-6x) = -8x.

Can I expand binomials in a different order?

Yes! You can multiply in any order and get the same answer. FOIL is just one systematic way that helps prevent mistakes. The key is to multiply each term in the first binomial by each term in the second.

What if I get the wrong sign on the middle term?

Double-check your Outside and Inside steps! For (x-6)(x-2): Outside gives x×(-2) = -2x, Inside gives (-6)×x = -6x. Combined: -2x + (-6x) = -8x.

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Convert f(x) = (x-6)(x-2) to Its Standard Quadratic Form

Expanding Binomials with FOIL Method

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What does FOIL stand for again?

Why is the constant term positive when both numbers are negative?

How do I know which terms are 'like terms' to combine?

Can I expand binomials in a different order?

What if I get the wrong sign on the middle term?

🌟 Unlock Your Math Potential

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