Solve a(ab+3): Evaluating the Expression When a=-1 and b=5

Q: Why do I substitute the values before doing any operations?

Substitution comes first! Replace each variable with its number value immediately. This prevents confusion and helps you see exactly what calculations to perform.

Q: How do I remember the sign rules for multiplying negative numbers?

Remember: same signs give positive, different signs give negative. So $ (-1) \times (-2) = +2 $ and $ (-1) \times (+5) = -5 $.

Q: What if I get confused with all the parentheses?

Work from the innermost parentheses outward. In $ a(ab + 3) $, solve $ ab + 3 $ first, then multiply by the outside $ a $.

Q: Can I check my answer somehow?

Yes! Substitute your values step-by-step: $ a = -1, b = 5 $ gives $ (-1)[(-1)(5) + 3] = (-1)[-5 + 3] = (-1)(-2) = 2 $ ✓

Q: Why is the answer positive when we start with negative numbers?

Because we end up with $ (-1) \times (-2) $! When you multiply two negative numbers, the result is always positive. This is a fundamental rule of arithmetic.

Algebraic Substitution with Negative Numbers

$a\cdot(a\cdot b+3)=$

Replace and calculate if $a=-1,b=5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's set up and calculate the problem.

00:11 We'll assign values based on the data we have. Remember to pay attention to parentheses.

00:38 A negative times a positive is always negative.

00:48 Always calculate what's inside the parentheses first.

01:00 A negative times a negative is always positive.

01:08 And that's how we find the solution to this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$a\cdot(a\cdot b+3)=$

Replace and calculate if $a=-1,b=5$

Step-by-step solution

Let's begin by inserting the numbers into the formula:

$-1\times(-1\times5+3)=$

We must remember the following rule:

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

Let's now solve the expression inside of the parentheses:

$(-1\times5+3)=$

$-1\times5=-5$

$-5+3=-2$

We should obtain the following expression:

$-1\times(-2)=$

Let's again remember the rule:

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

Therefore, the correct answer is:

$2$

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace each variable with its given value first
Order of Operations: Solve inside parentheses: $(-1)(5) + 3 = -5 + 3 = -2$
Sign Rules Check: Verify $(-1) \times (-2) = +2$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring the order of operations with parentheses
Don't solve $-1 \times (-1 \times 5 + 3)$ by multiplying -1 × -1 first = wrong answer +8! This violates order of operations. Always solve what's inside parentheses completely before multiplying by the outside factor.

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 do I substitute the values before doing any operations?

Substitution comes first! Replace each variable with its number value immediately. This prevents confusion and helps you see exactly what calculations to perform.

How do I remember the sign rules for multiplying negative numbers?

Remember: same signs give positive, different signs give negative. So $(-1) \times (-2) = +2$ and $(-1) \times (+5) = -5$ .

What if I get confused with all the parentheses?

Work from the innermost parentheses outward. In $a(ab + 3)$ , solve $ab + 3$ first, then multiply by the outside $a$ .

Can I check my answer somehow?

Yes! Substitute your values step-by-step: $a = -1, b = 5$ gives $(-1)[(-1)(5) + 3] = (-1)[-5 + 3] = (-1)(-2) = 2$ ✓

Why is the answer positive when we start with negative numbers?

Because we end up with $(-1) \times (-2)$ ! When you multiply two negative numbers, the result is always positive. This is a fundamental rule of arithmetic.

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