Solve (a+8)(b+7) - Missing Term = 7a+8b: Algebraic Expansion Challenge

Q: Why can't I just subtract 7a + 8b from the left side?

You can do that! When you subtract $ 7a + 8b $ from both sides of the expanded form, the $ 7a + 8b $ terms cancel out, leaving you with $ ab + 56 - ▭ = 0 $.

Q: What does the square symbol (▭) represent in this problem?

The square symbol ▭ represents the missing term that we need to find. It's the expression that, when subtracted from $ (a+8)(b+7) $, gives us $ 7a + 8b $.

Q: How do I remember the FOIL method correctly?

FOIL stands for: First terms: a × bOuter terms: a × 7Inner terms: 8 × bLast terms: 8 × 7 Then add all four products together!

Q: Why is ab + 56 the correct answer and not just 56?

Because when you expand $ (a+8)(b+7) $, you get four terms: ab + 7a + 8b + 56. To get just 7a + 8b, you must subtract both ab and 56, not just 56 alone.

Q: Can I check my answer by plugging in numbers?

Absolutely! Try a = 2, b = 3: $ (2+8)(3+7) = 100 $, and $ 100 - (2×3 + 56) = 100 - 62 = 38 $. Also, $ 7(2) + 8(3) = 38 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:04 Open parentheses properly, multiply each factor by each factor

00:14 Calculate the products

00:17 Isolate the unknown

00:26 Collect like terms

00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$(a+8)(b+7)-▭=7a+8b$

$▭=\text{?}$

2

Step-by-step solution

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

Step 1: Expand the expression $(a+8)(b+7)$ using the distributive property.
Step 2: Compare the expanded terms with $7a + 8b$ to find the missing part.
Step 3: Identify the correct expression to fill the blank.

Now, let's work through each step:
Step 1: Expand the expression $(a+8)(b+7)$ .
Using the distributive property: $(a+8)(b+7) = a(b+7) + 8(b+7)$ $= ab + 7a + 8b + 56$ Step 2: Compare the expanded terms with the given equation. We have: $ab + 7a + 8b + 56 - ▭ = 7a + 8b$ Subtract $7a + 8b$ from both sides: $ab + 7a + 8b + 56 - ▭ - 7a - 8b = 0$ This simplifies to: $ab + 56 - ▭ = 0$ Step 3: Solving for the missing part, we find: $▭ = ab + 56$ Therefore, the expression that fills in the blank is $ab+56$ .

The correct choice from the options provided is:

$ab+56$

3

Final Answer

$ab+56$

Key Points to Remember

Essential concepts to master this topic

Expansion: Use distributive property (a+8)(b+7) = ab + 7a + 8b + 56
Technique: Set up equation: ab + 7a + 8b + 56 - ▭ = 7a + 8b
Check: Verify (a+8)(b+7) - (ab+56) = 7a + 8b ✓

Common Mistakes

Avoid these frequent errors

Incorrectly expanding the binomial product
Don't just multiply the first terms and last terms = missing the middle terms! This gives incomplete expansion like ab + 56 instead of ab + 7a + 8b + 56. Always use FOIL or distributive property to expand all four terms completely.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

FAQ

Everything you need to know about this question

Why can't I just subtract 7a + 8b from the left side?

+

You can do that! When you subtract $7a + 8b$ from both sides of the expanded form, the $7a + 8b$ terms cancel out, leaving you with $ab + 56 - ▭ = 0$ .

What does the square symbol (▭) represent in this problem?

+

The square symbol ▭ represents the missing term that we need to find. It's the expression that, when subtracted from $(a+8)(b+7)$ , gives us $7a + 8b$ .

How do I remember the FOIL method correctly?

+

FOIL stands for:

First terms: a × b
Outer terms: a × 7
Inner terms: 8 × b
Last terms: 8 × 7

Then add all four products together!

Why is ab + 56 the correct answer and not just 56?

+

Because when you expand $(a+8)(b+7)$ , you get four terms: ab + 7a + 8b + 56. To get just 7a + 8b, you must subtract both ab and 56, not just 56 alone.

Can I check my answer by plugging in numbers?

+

Absolutely! Try a = 2, b = 3: $(2+8)(3+7) = 100$ , and $100 - (2×3 + 56) = 100 - 62 = 38$ . Also, $7(2) + 8(3) = 38$ ✓

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Solve (a+8)(b+7) - Missing Term = 7a+8b: Algebraic Expansion Challenge

Algebraic Expansion with Missing Terms

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