Solve (2x-y)(4-3x): Expanding Binomial Products Step-by-Step

Q: Why do I get a positive 3xy term when both factors are negative?

Great question! When you multiply (-y) × (-3x), you get a positive result because negative × negative = positive. So (-y)(-3x) = +3xy.

Q: How do I remember which terms to multiply together?

Use the FOIL method: First: (2x)(4) = 8xOuter: (2x)(-3x) = -6x²Inner: (-y)(4) = -4yLast: (-y)(-3x) = +3xy

Q: Why is my x² term negative when x terms are positive?

The $ x^2 $ coefficient comes from (2x)(-3x) = -6x². Even though both terms contain x, one has a negative sign, making the result negative!

Q: Do I need to arrange terms in a specific order?

While not required, it's helpful to write terms in descending degree order: $ -6x^2 + 8x + 3xy - 4y $. This makes it easier to spot patterns and check your work.

Q: What if I can't combine any like terms?

That's normal! In $ 8x - 6x^2 - 4y + 3xy $, all terms are different (different variables or powers), so none can be combined. Your final answer will have 4 separate terms.

Q: How can I check if my answer is correct?

Try substituting simple values like x = 1, y = 1 into both the original expression and your answer. If they give the same result, you're likely correct! For example: (2(1)-1)(4-3(1)) should equal your expanded form.

Binomial Multiplication with Mixed Terms

Solve the following equation:

$(2x-y)(4-3x)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Open parentheses properly, multiply each factor by each factor

00:27 Calculate the multiplications

00:57 Positive times negative always equals negative

01:04 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:

$(2x-y)(4-3x)=$

Step-by-step solution

We will use the expanded distributive law 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 distributive law. We will combine like terms if possible whilst taking into account the correct multiplication of signs:

$(2x-y)(4-3x)= \\ \boxed{8x-6x^2-4y+3xy}$ Therefore, the correct answer is answer C.

Final Answer

_{^{$8x-6x^2-4y+3xy$}}

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiplied systematically
Technique: $(2x)(-3x) = -6x^2$ and $(-y)(4) = -4y$
Check: Count terms: should have 4 products before combining like terms ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply all four term pairs
Don't skip terms like the (-y)(-3x) = +3xy term! Missing any of the four multiplications gives an incomplete answer. Always multiply First-Outer-Inner-Last systematically to get all four products before combining.

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 3xy term when both factors are negative?

Great question! When you multiply (-y) × (-3x), you get a positive result because negative × negative = positive. So (-y)(-3x) = +3xy.

How do I remember which terms to multiply together?

Use the FOIL method:

First: (2x)(4) = 8x
Outer: (2x)(-3x) = -6x²
Inner: (-y)(4) = -4y
Last: (-y)(-3x) = +3xy

Why is my x² term negative when x terms are positive?

The $x^2$ coefficient comes from (2x)(-3x) = -6x². Even though both terms contain x, one has a negative sign, making the result negative!

Do I need to arrange terms in a specific order?

While not required, it's helpful to write terms in descending degree order: $-6x^2 + 8x + 3xy - 4y$ . This makes it easier to spot patterns and check your work.

What if I can't combine any like terms?

That's normal! In $8x - 6x^2 - 4y + 3xy$ , all terms are different (different variables or powers), so none can be combined. Your final answer will have 4 separate terms.

How can I check if my answer is correct?

Try substituting simple values like x = 1, y = 1 into both the original expression and your answer. If they give the same result, you're likely correct! For example: (2(1)-1)(4-3(1)) should equal your expanded form.

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