Solve a·b+b: Substituting Values a=-3 and b=-2

Q: Why does multiplying two negatives give a positive?

Think of it as "opposite of opposite". When you multiply $ (-3) \times (-2) $, you're taking the opposite of 3, then the opposite again, which brings you back to positive: $ +6 $.

Q: Should I always use parentheses when substituting?

Yes, especially with negative numbers! Writing $ a \cdot b + b $ as $ (-3) \times (-2) + (-2) $ prevents sign confusion and calculation errors.

Q: What's the difference between +(-2) and -2?

They're mathematically the same! $ +(-2) = -2 $. The expression $ 6 + (-2) $ can be written as $ 6 - 2 $ for easier calculation.

Q: How do I know which operation to do first?

Follow order of operations (PEMDAS)! In $ a \cdot b + b $, multiplication comes before addition, so calculate $ (-3) \times (-2) = 6 $ first, then add $ 6 + (-2) = 4 $.

Q: Can I factor out b to make it easier?

Great thinking! Yes, $ a \cdot b + b = b(a + 1) $. With our values: $ (-2)((-3) + 1) = (-2)(-2) = 4 $. Same answer, different path!

Algebraic Substitution with Negative Numbers

$a\cdot b+b=$

Solve the following problem if:

$a=-3,b=-2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 First, set up the problem, then calculate the answer.

00:13 Let's substitute the right values, following the data carefully. Remember to use parentheses correctly.

00:35 Remember, negative times negative equals positive.

00:49 And positive times negative equals negative.

00:53 That's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$a\cdot b+b=$

Solve the following problem if:

$a=-3,b=-2$

Step-by-step solution

Let's substitute the numbers into the formula:

$-3\times(-2)+(-2)=$

Remember the rule:

$(-x)\times(-x)=+x$

First, let's solve the multiplication problem:

$-3\times-2=6$

We obtain the following expression:

$6+(-2)=$

Let's remember the rule:

$+(-x)=-x$

Let's write the expression in the appropriate form:

$6-2=$

Therefore, the answer is:

$4$

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Rule: Replace variables with given values carefully preserving signs
Technique: Calculate $(-3) \times (-2) = +6$ first, then add
Check: Verify $6 + (-2) = 4$ matches the answer ✓

Common Mistakes

Avoid these frequent errors

Forgetting to use parentheses when substituting negative values
Don't write -3×-2+-2 without parentheses = confusion with signs! Missing parentheses leads to sign errors and wrong calculations. Always use parentheses: (-3)×(-2)+(-2) to keep track of negative signs.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$(+6)\cdot(+9)=$

FAQ

Everything you need to know about this question

Why does multiplying two negatives give a positive?

Think of it as "opposite of opposite". When you multiply $(-3) \times (-2)$ , you're taking the opposite of 3, then the opposite again, which brings you back to positive: $+6$ .

Should I always use parentheses when substituting?

Yes, especially with negative numbers! Writing $a \cdot b + b$ as $(-3) \times (-2) + (-2)$ prevents sign confusion and calculation errors.

What's the difference between +(-2) and -2?

They're mathematically the same! $+(-2) = -2$ . The expression $6 + (-2)$ can be written as $6 - 2$ for easier calculation.

How do I know which operation to do first?

Follow order of operations (PEMDAS)! In $a \cdot b + b$ , multiplication comes before addition, so calculate $(-3) \times (-2) = 6$ first, then add $6 + (-2) = 4$ .

Can I factor out b to make it easier?

Great thinking! Yes, $a \cdot b + b = b(a + 1)$ . With our values: $(-2)((-3) + 1) = (-2)(-2) = 4$ . Same answer, different path!

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