Solve the Expression: a + b(a+1) with a=2 and b=-3

Q: Why do I get a negative answer when one of the values is positive?

The negative coefficient $ b=-3 $ creates a negative product when multiplied. Since $ -3 \times 3 = -9 $ and $ 2 - 9 = -7 $, the final result is negative.

Q: Do I need to write +(-3) or can I just write -3?

Both are correct! $ +(-3) = -3 $ by the sign rules. Writing $ 2-3\times(2+1) $ is cleaner and easier to work with.

Q: What if I forget to solve the parentheses first?

You'll get the wrong answer! Order of operations (PEMDAS) requires parentheses first. If you multiply before solving $ (2+1) $, your calculation will be incorrect.

Q: How do I check if my substitution is correct?

Replace each variable carefully: $ a $ becomes $ 2 $ everywhere, and $ b $ becomes $ -3 $ everywhere. Then follow order of operations step by step.

Q: Why is the answer -7 and not 7?

The negative comes from $ -3 \times 3 = -9 $. Since we have $ 2 + (-9) = 2 - 9 = -7 $, the final answer must be negative.

Variable Substitution with Negative Coefficients

$a+b\cdot(a+1)=$

Replace and calculate if $a=2,b=-3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's set up our equation and calculate step by step.

00:13 We'll put in the right values as given. Remember to always notice those parentheses.

00:39 A positive number times a negative one, will always give a negative result.

00:46 Next, calculate everything that's inside the parentheses first.

00:52 Remember to do multiplication and division before moving on to addition and subtraction.

00:58 Let's keep solving this, following the correct order of operations.

01:02 And that's how we find the solution to our question. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$a+b\cdot(a+1)=$

Replace and calculate if $a=2,b=-3$

Step-by-step solution

Let's substitute the numbers into the formula:

$2+(-3)\times(2+1)=$

Let's remember the rule:

$+(-x)=-x$

Let's write the exercise in the appropriate form:

$2-3\times(2+1)=$

Let's solve the expression in parentheses:

$2+1=3$

Now we get the exercise:

$2-3\times3=$

Now let's solve the multiplication exercise:

$3\times3=9$

Now we get the exercise:

$2-9=$

Therefore, the answer is:

$-7$

Final Answer

$-7$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Solve parentheses first, then multiply, finally add/subtract
Technique: Substitute $a=2, b=-3$ to get $2+(-3)\times(2+1)$
Check: Verify each step: parentheses first (3), then multiply (-9), finally add (2-9=-7) ✓

Common Mistakes

Avoid these frequent errors

Adding before multiplying in order of operations
Don't calculate 2+(-3) first = -1×3 = -3! This ignores the multiplication priority and gives the wrong answer. Always follow PEMDAS: solve parentheses (2+1=3), then multiply (-3×3=-9), then add/subtract (2-9=-7).

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 do I get a negative answer when one of the values is positive?

The negative coefficient $b=-3$ creates a negative product when multiplied. Since $-3 \times 3 = -9$ and $2 - 9 = -7$ , the final result is negative.

Do I need to write +(-3) or can I just write -3?

Both are correct! $+(-3) = -3$ by the sign rules. Writing $2-3\times(2+1)$ is cleaner and easier to work with.

What if I forget to solve the parentheses first?

You'll get the wrong answer! Order of operations (PEMDAS) requires parentheses first. If you multiply before solving $(2+1)$ , your calculation will be incorrect.

How do I check if my substitution is correct?

Replace each variable carefully: $a$ becomes $2$ everywhere, and $b$ becomes $-3$ everywhere. Then follow order of operations step by step.

Why is the answer -7 and not 7?

The negative comes from $-3 \times 3 = -9$ . Since we have $2 + (-9) = 2 - 9 = -7$ , the final answer must be negative.

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