Calculate (7+8)² : Square of Sum Expression

Q: Why can't I just square each number separately?

Because squaring a sum is different from summing squares! When you have $ (7+8)^2 $, you're squaring the entire sum (15), not each part. The formula $ (a+b)^2 = a^2 + 2ab + b^2 $ shows you need that middle term 2ab.

Q: What does the middle term 2ab represent?

The 2ab term comes from multiplying the binomial by itself: $ (a+b)(a+b) $. When you use FOIL, you get ab + ba = 2ab. In our case, $ 2 \times 7 \times 8 = 112 $.

Q: How can I remember this formula?

Think "First, Outer, Inner, Last" when expanding $ (a+b)(a+b) $:First: $ a \times a = a^2 $Outer + Inner: $ a \times b + b \times a = 2ab $Last: $ b \times b = b^2 $

Q: Should I always expand or can I just calculate 15²?

It depends on what the question asks! If it wants the expanded form, show $ 7^2 + 2 \times 7 \times 8 + 8^2 $. If it wants the numerical answer, calculate $ 15^2 = 225 $.

Q: Does this work for subtraction too?

Yes! For $ (a-b)^2 $, the formula becomes $ a^2 - 2ab + b^2 $. Notice the middle term is negative when you have subtraction in the original expression.

Square of Sum Formula with Binomial Expansion

$(7+8)^2=\text{?}$

❤️ 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 open the parentheses

00:13 In our exercise 7 is A

00:18 and 8 is B

00:23 Let's substitute according to the formula

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

$(7+8)^2=\text{?}$

Step-by-step solution

To solve this problem, we'll use the formula for the square of a sum.

Step 1: Identify our variables as $a = 7$ and $b = 8$ .
Step 2: Apply the formula $(a + b)^2 = a^2 + 2ab + b^2$ .
Step 3: Substitute into the formula:
$(7 + 8)^2 = 7^2 + 2 \times 7 \times 8 + 8^2$ .
Step 4: Express the final expression in the most informative form.

Therefore, the expanded expression for $(7 + 8)^2$ is $7^2 + 2 \times 7 \times 8 + 8^2$ .

Regarding the choices provided, the correct one is Option 3: $7^2 + 2 \times 7 \times 8 + 8^2$ .

Final Answer

$7^2+2\times7\times8+8^2$

Key Points to Remember

Essential concepts to master this topic

Formula: $(a + b)^2 = a^2 + 2ab + b^2$ creates three terms
Technique: Substitute a=7, b=8: $7^2 + 2(7)(8) + 8^2$
Check: Calculate both ways: $(7+8)^2 = 15^2 = 225$ and expansion equals 225 ✓

Common Mistakes

Avoid these frequent errors

Using only the squared terms without the middle term
Don't think $(7+8)^2 = 7^2 + 8^2$ = 49 + 64 = 113! This misses the crucial middle term 2ab = 112. Always include all three terms: $a^2 + 2ab + b^2$ .

Practice Quiz

Test your knowledge with interactive questions

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

$$ (x+y)^2 $$

FAQ

Everything you need to know about this question

Why can't I just square each number separately?

Because squaring a sum is different from summing squares! When you have $(7+8)^2$ , you're squaring the entire sum (15), not each part. The formula $(a+b)^2 = a^2 + 2ab + b^2$ shows you need that middle term 2ab.

What does the middle term 2ab represent?

The 2ab term comes from multiplying the binomial by itself: $(a+b)(a+b)$ . When you use FOIL, you get ab + ba = 2ab. In our case, $2 \times 7 \times 8 = 112$ .

How can I remember this formula?

Think "First, Outer, Inner, Last" when expanding $(a+b)(a+b)$ :

First: $a \times a = a^2$
Outer + Inner: $a \times b + b \times a = 2ab$
Last: $b \times b = b^2$

Should I always expand or can I just calculate 15²?

It depends on what the question asks! If it wants the expanded form, show $7^2 + 2 \times 7 \times 8 + 8^2$ . If it wants the numerical answer, calculate $15^2 = 225$ .

Does this work for subtraction too?

Yes! For $(a-b)^2$ , the formula becomes $a^2 - 2ab + b^2$ . Notice the middle term is negative when you have subtraction in the original expression.

🌟 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