Solve -a(b+2): Evaluating Expression When a=-5 and b=6

Q: Why does -(-5) equal +5?

The double negative rule states that two negatives make a positive! Think of it as: the negative of negative 5 is positive 5. It's like saying "not negative" which means positive.

Q: Do I always solve parentheses first?

Yes! Follow PEMDAS/BODMAS order of operations. Always solve what's inside parentheses first, then handle multiplication. So (6+2) = 8 before multiplying by 5.

Q: What if I forgot the double negative and got -40?

That's the most common mistake! You would have calculated $ -5 \times 8 = -40 $ instead of $ +5 \times 8 = +40 $. Always check: does your expression have -(-x)?

Q: How can I remember the double negative rule?

Think of real life: if you don't have no money, that means you do have money! Similarly, if you don't have negative 5, you have positive 5.

Q: Should I substitute both variables at the same time?

Yes, but be careful with signs! Replace a with -5 and b with 6 in the same step: $ -a(b+2) $ becomes $ -(-5)(6+2) $.

Expression Evaluation with Negative Variable Substitution

Solve the following expression:

$-a\cdot(b+2)=$

If $a=-5,\text{ }b=6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Place and calculate

00:05 We'll substitute appropriate values according to the given data, being careful with parentheses

00:17 Negative times negative always equals positive

00:23 Let's calculate the parentheses

00:26 Let's calculate the multiplication

00:29 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

Solve the following expression:

$-a\cdot(b+2)=$

If $a=-5,\text{ }b=6$

Step-by-step solution

Let's substitute the numbers into the formula:

$-(-5)\times(6+2)=$

Let's remember the rule:

$-(-x)=+x$

Let's write the exercise in the appropriate form:

$5\times(6+2)=$

Let's solve the expression in parentheses:

$6+2=8$

We obtain the following exercise:

$5\times8=$

Therefore, the answer is:

$40$

Final Answer

$40$

Key Points to Remember

Essential concepts to master this topic

Double Negative Rule: When substituting negative values, -(-x) becomes +x
Technique: Substitute a = -5: -(-5)(6+2) = 5(8) = 40
Check: Verify order of operations: parentheses first, then multiplication ✓

Common Mistakes

Avoid these frequent errors

Forgetting to apply the double negative rule
Don't substitute -5 directly without considering the negative sign: -a becomes -(-5) = +5, not just -5! This changes the entire calculation from negative to positive. Always recognize that -(-x) = +x when substituting negative values.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why does -(-5) equal +5?

The double negative rule states that two negatives make a positive! Think of it as: the negative of negative 5 is positive 5. It's like saying "not negative" which means positive.

Do I always solve parentheses first?

Yes! Follow PEMDAS/BODMAS order of operations. Always solve what's inside parentheses first, then handle multiplication. So (6+2) = 8 before multiplying by 5.

What if I forgot the double negative and got -40?

That's the most common mistake! You would have calculated $-5 \times 8 = -40$ instead of $+5 \times 8 = +40$ . Always check: does your expression have -(-x)?

How can I remember the double negative rule?

Think of real life: if you don't have no money, that means you do have money! Similarly, if you don't have negative 5, you have positive 5.

Should I substitute both variables at the same time?

Yes, but be careful with signs! Replace a with -5 and b with 6 in the same step: $-a(b+2)$ becomes $-(-5)(6+2)$ .

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