Solve (2x+3)(-5-x): Binomial Expression Multiplication

Q: Why do I get so many negative signs in my answer?

The second binomial $ (-5-x) $ has all negative terms! When you multiply anything by negative values, you get negative results. This is why the final answer has mostly negative terms.

Q: How do I keep track of all the multiplication steps?

Use the FOIL method systematically: First terms, Outer terms, Inner terms, Last terms. Write each step: $ -10x - 2x^2 - 15 - 3x $, then combine like terms.

Q: What if I accidentally change the signs when combining terms?

Be extra careful with negative coefficients! Underline or circle each negative sign as you work. Remember: $ -10x - 3x = -13x $, not $ -7x $.

Q: Can I rearrange the binomials before multiplying?

Yes! $ (2x+3)(-5-x) $ equals $ (-5-x)(2x+3) $ by the commutative property. However, keep the same order to avoid confusion with signs.

Q: Why is my answer a quadratic expression?

When you multiply two linear expressions, you get a quadratic! The highest degree term comes from multiplying the variable terms: $ (2x) \cdot (-x) = -2x^2 $.

Binomial Multiplication with Negative Terms

Solve the following equation:

$(2x+3)(-5-x)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

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

00:28 Let's calculate the multiplications

01:00 Positive times negative always equals negative

01:13 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

Solve the following equation:

$(2x+3)(-5-x)=$

Step-by-step solution

We will use the extended distribution law as seen below in order to simplify the given expression:

$(a+b)(c+d)=ac+ad+bc+bd$

We will begin by performing the multiplication between the pairs of parentheses, using the mentioned distribution law. Then we will proceed to combine like terms if possible. We'll do this whilst taking into account the correct multiplication of signs:

$(2x+3)(-5-x)= \\ -10x-2x^2-15-3x=\\ \boxed{-2x^2-13x-15}$

Therefore, the correct answer is answer D.

Final Answer

_{$-2x^2-13x-15$}

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply (a+b)(c+d) = ac+ad+bc+bd systematically
Technique: (2x+3)(-5-x) = (2x)(-5) + (2x)(-x) + (3)(-5) + (3)(-x)
Check: Substitute x=1: -2(1)²-13(1)-15 = -30, verify with original expression ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute all terms completely
Don't just multiply first terms and ignore others = incomplete expansion! This misses crucial terms like -2x² and gives wrong degree polynomial. Always multiply each term in first binomial by every term in second binomial.

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 so many negative signs in my answer?

The second binomial $(-5-x)$ has all negative terms! When you multiply anything by negative values, you get negative results. This is why the final answer has mostly negative terms.

How do I keep track of all the multiplication steps?

Use the FOIL method systematically: First terms, Outer terms, Inner terms, Last terms. Write each step: $-10x - 2x^2 - 15 - 3x$ , then combine like terms.

What if I accidentally change the signs when combining terms?

Be extra careful with negative coefficients! Underline or circle each negative sign as you work. Remember: $-10x - 3x = -13x$ , not $-7x$ .

Can I rearrange the binomials before multiplying?

Yes! $(2x+3)(-5-x)$ equals $(-5-x)(2x+3)$ by the commutative property. However, keep the same order to avoid confusion with signs.

Why is my answer a quadratic expression?

When you multiply two linear expressions, you get a quadratic! The highest degree term comes from multiplying the variable terms: $(2x) \cdot (-x) = -2x^2$ .

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