Solve (+4x)×(-4x): Multiplying Terms with Same Variables

Q: Why is the answer negative when both terms have x?

The sign comes from multiplying the coefficients, not the variables! We have $ (+4) \times (-4) = -16 $, so the result is negative.

Q: How do I know when to add the exponents?

When you multiply variables with the same base, you add their exponents. Since both terms have $ x^1 $, we get $ x^{1+1} = x^2 $.

Q: What if one coefficient was positive and one was positive?

If both coefficients are positive, like $ (+4x) \times (+4x) $, then you'd get $ +16x^2 $. Positive times positive equals positive!

Q: Can I multiply the x's first, then the numbers?

Yes! You can multiply in any order due to the commutative property. Whether you do coefficients first or variables first, you'll get the same answer.

Q: Why isn't the answer just -8x?

That would be adding the terms: $ 4x + (-4x) = 0 $. But we're multiplying, which gives us $ -16x^2 $ with a squared variable!

Monomial Multiplication with Negative Coefficients

$(+4x)\times(-4x)=$

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Step-by-step video solution

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00:00 Simply

00:03 Negative times negative is always positive

00:06 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$(+4x)\times(-4x)=$

Step-by-step solution

Let's solve this problem step-by-step:

Step 1: Multiply the coefficients: Take the coefficients of the terms $+4$ and $-4$ . Multiplying these, we get $4 \times -4 = -16$ .
Step 2: Multiply the variables: The term contains the variable $x$ . Using the property of exponents, $x^1 \times x^1 = x^{1+1} = x^2$ .
Step 3: Write the combined expression: Combine the outcomes from Steps 1 and 2: $-16x^2$ .

Hence, the expression $(+4x)\times(-4x)$ simplifies to $-16x^2$ .

Therefore, the correct solution to the problem is $-16x^2$ .

Final Answer

$-16x^2$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive times negative gives negative result
Technique: Multiply coefficients: $4 \times (-4) = -16$ , then variables: $x \times x = x^2$
Check: Verify coefficient sign and variable exponent: $-16x^2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign when multiplying coefficients
Don't ignore the negative sign and write $16x^2$ instead of $-16x^2$ ! Positive times negative must give negative. Always apply the sign rules carefully: $(+4) \times (-4) = -16$ .

Practice Quiz

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Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why is the answer negative when both terms have x?

The sign comes from multiplying the coefficients, not the variables! We have $(+4) \times (-4) = -16$ , so the result is negative.

How do I know when to add the exponents?

When you multiply variables with the same base, you add their exponents. Since both terms have $x^1$ , we get $x^{1+1} = x^2$ .

What if one coefficient was positive and one was positive?

If both coefficients are positive, like $(+4x) \times (+4x)$ , then you'd get $+16x^2$ . Positive times positive equals positive!

Can I multiply the x's first, then the numbers?

Yes! You can multiply in any order due to the commutative property. Whether you do coefficients first or variables first, you'll get the same answer.

Why isn't the answer just -8x?

That would be adding the terms: $4x + (-4x) = 0$ . But we're multiplying, which gives us $-16x^2$ with a squared variable!

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