Solve Expression a·b+1 When a=2 and b=-2: Step-by-Step

Q: Why is 2×(-2) equal to -4 and not +4?

When you multiply a positive number by a negative number, the result is always negative. Think of it as: positive × negative = negative. So $ 2 \times (-2) = -4 $.

Q: What if I accidentally did the addition first?

If you calculated $ 2 \times (-2+1) = 2 \times (-1) = -2 $, you'd get the wrong answer! Remember: multiplication comes before addition in order of operations (PEMDAS).

Q: How can I remember the sign rules for multiplication?

Same signs: positive × positive = positive, negative × negative = positiveDifferent signs: positive × negative = negative, negative × positive = negative

Q: Should I double-check my final calculation?

Absolutely! Substitute back: $ a \cdot b + 1 = 2 \times (-2) + 1 = -4 + 1 = -3 $. This confirms our answer is correct.

Algebraic Substitution with Negative Numbers

$a\cdot b+1=$

Replace and calculate if $a=2,b=-2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Place and calculate

00:04 Let's substitute appropriate values according to the given data, being careful with parentheses

00:19 Positive times negative is always negative

00:23 Let's continue solving according to the correct order of operations

00:27 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

$a\cdot b+1=$

Replace and calculate if $a=2,b=-2$

Step-by-step solution

Let's begin by inserting the given data into the formula:

$2\times(-2)+1=$

Remembering the rule:

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

Let's now solve the multiplication operation:

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

In order to obtain the following expression:

$-4+1=$

Therefore, the answer is:

$-3$

Final Answer

$-3$

Key Points to Remember

Essential concepts to master this topic

Substitution: Replace variables with given values: a=2, b=-2
Multiplication: Positive times negative equals negative: 2×(-2)=-4
Check: Verify order of operations: multiply first, then add ✓

Common Mistakes

Avoid these frequent errors

Adding before multiplying
Don't calculate a+1 first, then multiply by b = wrong order! This ignores order of operations and gives incorrect results. Always multiply a·b first, then add 1.

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 is 2×(-2) equal to -4 and not +4?

When you multiply a positive number by a negative number, the result is always negative. Think of it as: positive × negative = negative. So $2 \times (-2) = -4$ .

Do I need to use parentheses when substituting negative values?

Yes! Always put parentheses around negative values when substituting: $2 \times (-2)$ . This prevents confusion and helps you apply the correct multiplication rules.

What if I accidentally did the addition first?

If you calculated $2 \times (-2+1) = 2 \times (-1) = -2$ , you'd get the wrong answer! Remember: multiplication comes before addition in order of operations (PEMDAS).

How can I remember the sign rules for multiplication?

Same signs: positive × positive = positive, negative × negative = positive
Different signs: positive × negative = negative, negative × positive = negative

Should I double-check my final calculation?

Absolutely! Substitute back: $a \cdot b + 1 = 2 \times (-2) + 1 = -4 + 1 = -3$ . This confirms our answer is correct.

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