Express (x-6)² + 2x in Standard Function Form

Q: How do I remember the perfect square formula?

Think of it as FOIL with identical binomials! $ (x-6)^2 = (x-6)(x-6) $. First: $ x \cdot x = x^2 $, Outer + Inner: $ -6x + (-6x) = -12x $, Last: $ (-6)(-6) = 36 $.

Q: Why do I get different answers when I don't combine like terms?

Standard form requires all like terms combined! If you leave $ x^2 - 12x + 36 + 2x $ as is, it's not simplified. Always combine $ -12x + 2x = -10x $ to get the final answer.

Q: Can I expand this differently?

You could use distribution twice: $ (x-6)(x-6) $ then FOIL, but the perfect square formula $ (a-b)^2 = a^2 - 2ab + b^2 $ is faster and less error-prone!

Q: What if I forget to add the 2x term?

You'll get $ x^2 - 12x + 36 $ instead of the correct $ x^2 - 10x + 36 $! Always read the entire expression carefully and don't miss any terms.

Q: How do I check my final answer?

Substitute a simple value like $ x = 0 $ into both forms. Original: $ (0-6)^2 + 2(0) = 36 $. Your answer: $ 0^2 - 10(0) + 36 = 36 $. They match!

Expanding Quadratics with Linear Terms

Find the standard representation of the following function

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

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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 Expand brackets using shortened multiplication formulas

00:08 Calculate powers and products

00:18 Group factors

00:30 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

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

Step-by-step solution

To solve this problem, we'll transform the given expression into standard quadratic form by expanding and simplifying:

Step 1: Expand $(x - 6)^2$
$(x - 6)^2 = x^2 - 12x + 36$
Step 2: Add $2x$
$f(x) = x^2 - 12x + 36 + 2x$
Step 3: Simplify
Combine like terms: $-12x + 2x = -10x$ , resulting in the expression:
$f(x) = x^2 - 10x + 36$

Therefore, the standard form of the function $f(x)$ is $x^2 - 10x + 36$ . This corresponds to choice 1 in the given list.

Thus, the final solution is $f(x) = x^2 - 10x + 36$ .

Final Answer

$f(x)=x^2-10x+36$

Key Points to Remember

Essential concepts to master this topic

Rule: Expand perfect squares using $(a-b)^2 = a^2 - 2ab + b^2$
Technique: $(x-6)^2 = x^2 - 12x + 36$ then add $2x$
Check: Combine like terms: $-12x + 2x = -10x$ gives $x^2 - 10x + 36$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly expanding the perfect square
Don't write $(x-6)^2 = x^2 + 36$ forgetting the middle term = wrong final answer! This misses the crucial $-2(x)(6) = -12x$ term from the perfect square formula. Always use $(a-b)^2 = a^2 - 2ab + b^2$ completely.

Practice Quiz

Test your knowledge with interactive questions

Create an algebraic expression based on the following parameters:

$$ a=3,b=0,c=-3 $$

FAQ

Everything you need to know about this question

How do I remember the perfect square formula?

Think of it as FOIL with identical binomials! $(x-6)^2 = (x-6)(x-6)$ . First: $x \cdot x = x^2$ , Outer + Inner: $-6x + (-6x) = -12x$ , Last: $(-6)(-6) = 36$ .

Why do I get different answers when I don't combine like terms?

Standard form requires all like terms combined! If you leave $x^2 - 12x + 36 + 2x$ as is, it's not simplified. Always combine $-12x + 2x = -10x$ to get the final answer.

Can I expand this differently?

You could use distribution twice: $(x-6)(x-6)$ then FOIL, but the perfect square formula $(a-b)^2 = a^2 - 2ab + b^2$ is faster and less error-prone!

What if I forget to add the 2x term?

You'll get $x^2 - 12x + 36$ instead of the correct $x^2 - 10x + 36$ ! Always read the entire expression carefully and don't miss any terms.

How do I check my final answer?

Substitute a simple value like $x = 0$ into both forms. Original: $(0-6)^2 + 2(0) = 36$ . Your answer: $0^2 - 10(0) + 36 = 36$ . They match!

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Express (x-6)² + 2x in Standard Function Form

Expanding Quadratics with Linear Terms

❤️ 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

How do I remember the perfect square formula?

Why do I get different answers when I don't combine like terms?

Can I expand this differently?

What if I forget to add the 2x term?

How do I check my final answer?

🌟 Unlock Your Math Potential

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