Expand (a+b)²: Step-by-Step Perfect Square Formula

Q: Why is there a 2 in front of ab?

When you multiply $ (a+b)(a+b) $, you get two identical cross terms: $ a \cdot b $ and $ b \cdot a $. Since $ ab + ba = 2ab $, that's where the 2 comes from!

Q: Can I use this formula with numbers instead of letters?

Absolutely! For example, $ (3+4)^2 = 3^2 + 2(3)(4) + 4^2 = 9 + 24 + 16 = 49 $. The formula works with any values!

Q: What if I have (a-b)² instead?

Use the similar formula: $ (a-b)^2 = a^2 - 2ab + b^2 $. Notice the middle term becomes negative because you're subtracting b.

Q: How do I remember this formula?

Think "First, Last, Twice the Middle": square the first term, square the last term, then add twice the product of both terms together.

Q: Is this the same as the FOIL method?

Yes! $ (a+b)^2 = (a+b)(a+b) $. Using FOIL: First: $ a^2 $, Outer: $ ab $, Inner: $ ba $, Last: $ b^2 $ gives the same result.

Perfect Square Expansion with Binomial Terms

$(a+b)^2=\text{?}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve using shortened multiplication formulas

00:03 We will use shortened multiplication formulas to expand the brackets

00:09 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

$(a+b)^2=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Identify the given expression $(a+b)^2$ .
Apply the formula for the square of a sum: $(x+y)^2 = x^2 + 2xy + y^2$ .
Substitute $x = a$ and $y = b$ into the formula and simplify.

Let's apply these steps to the expression $(a+b)^2$ :
We start with the expression $(a+b)^2$ . This means we are squaring the sum $a + b$ .

According to the formula $(x+y)^2 = x^2 + 2xy + y^2$ , we can substitute $x = a$ and $y = b$ . Therefore, the expression becomes:

$(a+b)^2 = a^2 + 2ab + b^2$ .

Therefore, the expanded form of the expression $(a+b)^2$ is $a^2 + 2ab + b^2$ .

Final Answer

$a^2+2ab+b^2$

Key Points to Remember

Essential concepts to master this topic

Formula: $(a+b)^2 = a^2 + 2ab + b^2$ for any two terms
Pattern: First squared + twice the product + second squared
Verification: Multiply $(a+b)(a+b)$ using FOIL method to confirm ✓

Common Mistakes

Avoid these frequent errors

Forgetting the middle term 2ab
Don't write $(a+b)^2 = a^2 + b^2$ = missing the cross terms! This ignores the multiplication between different variables and gives an incomplete expansion. Always include the middle term $2ab$ when squaring a binomial.

Practice Quiz

Test your knowledge with interactive questions

Choose the expression that has the same value as the following:

$$ (x+3)^2 $$

FAQ

Everything you need to know about this question

Why is there a 2 in front of ab?

When you multiply $(a+b)(a+b)$ , you get two identical cross terms: $a \cdot b$ and $b \cdot a$ . Since $ab + ba = 2ab$ , that's where the 2 comes from!

Can I use this formula with numbers instead of letters?

Absolutely! For example, $(3+4)^2 = 3^2 + 2(3)(4) + 4^2 = 9 + 24 + 16 = 49$ . The formula works with any values!

What if I have (a-b)² instead?

Use the similar formula: $(a-b)^2 = a^2 - 2ab + b^2$ . Notice the middle term becomes negative because you're subtracting b.

How do I remember this formula?

Think "First, Last, Twice the Middle": square the first term, square the last term, then add twice the product of both terms together.

Is this the same as the FOIL method?

Yes! $(a+b)^2 = (a+b)(a+b)$ . Using FOIL: First: $a^2$ , Outer: $ab$ , Inner: $ba$ , Last: $b^2$ gives the same result.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Short Multiplication Formulas questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime