Multiply Binomials: Expanding (-13-z)(-2-x) Step by Step

Q: Why do I get a positive answer when multiplying two negative binomials?

Each multiplication in FOIL involves negative × negative = positive! Since (-13-z)(-2-x) has all negative terms, every product becomes positive: (-13)(-2) = +26, (-13)(-x) = +13x, (-z)(-2) = +2z, (-z)(-x) = +zx.

Q: What does FOIL stand for and why do I need it?

FOIL means First, Outer, Inner, Last. It ensures you multiply every term in the first binomial by every term in the second binomial. Without FOIL, you might miss some products and get the wrong answer.

Q: How do I keep track of all the negative signs?

Write out each multiplication step clearly: (-13)(-2), (-13)(-x), (-z)(-2), and (-z)(-x). Remember: negative times negative always equals positive!

Q: Can I check my answer by substituting numbers?

Yes! Try z = 1, x = 1: (-13-1)(-2-1) = (-14)(-3) = 42. Your expanded answer: (1)(1) + 13(1) + 2(1) + 26 = 1 + 13 + 2 + 26 = 42 ✓

Binomial Multiplication with Negative Terms

$(-13-z)(-2-x)=$

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Step-by-step video solution

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00:00 Solve

00:03 Open parentheses properly, multiply each factor by each factor

00:30 Calculate the products

00:51 Arrange the expression

00:59 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

$(-13-z)(-2-x)=$

Step-by-step solution

To solve the expression $(-13-z)(-2-x)$ , we will expand it using the distributive property (FOIL):

Step 1: Multiply the first terms:
$(-13) \cdot (-2) = 26$

Step 2: Multiply the outer terms:
$(-13) \cdot (-x) = 13x$

Step 3: Multiply the inner terms:
$(-z) \cdot (-2) = 2z$

Step 4: Multiply the last terms:
$(-z) \cdot (-x) = zx$

Now, combine all these results:
$26 + 13x + 2z + zx$

Therefore, the expanded form is $zx + 13x + 2z + 26$ .

The correct answer matches choice (1): $zx + 13x + 2z + 26$ .

Final Answer

$zx +13x+2z +26$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiply systematically
Sign Rule: Negative times negative equals positive: (-13)(-2) = +26
Check: Count four products and combine like terms properly ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply all four term combinations
Don't just multiply (-13)(-2) and (-z)(-x) = incomplete expansion! You miss the outer and inner terms, getting wrong results like -26-zx. Always use FOIL to multiply all four combinations: First, Outer, Inner, Last.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

Why do I get a positive answer when multiplying two negative binomials?

Each multiplication in FOIL involves negative × negative = positive! Since (-13-z)(-2-x) has all negative terms, every product becomes positive: (-13)(-2) = +26, (-13)(-x) = +13x, (-z)(-2) = +2z, (-z)(-x) = +zx.

What does FOIL stand for and why do I need it?

FOIL means First, Outer, Inner, Last. It ensures you multiply every term in the first binomial by every term in the second binomial. Without FOIL, you might miss some products and get the wrong answer.

How do I keep track of all the negative signs?

Write out each multiplication step clearly: (-13)(-2), (-13)(-x), (-z)(-2), and (-z)(-x). Remember: negative times negative always equals positive!

Why is the answer written as zx + 13x + 2z + 26 instead of 26 + 13x + 2z + zx?

Both are correct! The answer can be written in any order since we're just adding terms. However, standard form usually puts variable terms first, ordered by degree: zx (degree 2), then 13x and 2z (degree 1), then 26 (degree 0).

Can I check my answer by substituting numbers?

Yes! Try z = 1, x = 1: (-13-1)(-2-1) = (-14)(-3) = 42. Your expanded answer: (1)(1) + 13(1) + 2(1) + 26 = 1 + 13 + 2 + 26 = 42 ✓

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