Expand the Expression: (2y-3)(y-4) Using Binomial Multiplication

Q: Why do I keep getting the wrong sign on my constant term?

This happens when you forget that negative times negative equals positive! In $ (-3) \times (-4) $, both numbers are negative, so the result is positive 12, not negative 12.

Q: What's the easiest way to remember FOIL?

First terms, Outer terms, Inner terms, Last terms. For $ (2y-3)(y-4) $: First = $ 2y \cdot y $, Outer = $ 2y \cdot (-4) $, Inner = $ (-3) \cdot y $, Last = $ (-3) \cdot (-4) $.

Q: How do I combine the middle terms correctly?

Add the coefficients of like terms: $ -8y + (-3y) = -8y - 3y = -11y $. Remember that adding a negative is the same as subtracting!

Q: Can I check my answer by substituting a value?

Yes! Pick any value for y (like y = 1). Check: $ (2(1)-3)(1-4) = (-1)(-3) = 3 $ and $ 2(1)^2-11(1)+12 = 2-11+12 = 3 $. Both equal 3 ✓

Q: What if I get confused with all the negative signs?

Write each step clearly and use parentheses! For example: $ 2y^2 + (-8y) + (-3y) + 12 $. This makes it easier to see that you're adding negative terms.

Binomial Multiplication with Negative Terms

Solve the exercise:

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

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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 products

00:52 Positive times negative always equals negative

01:01 Collect terms

01:07 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 exercise:

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

Step-by-step solution

To solve the algebraic expression $(2y-3)(y-4)$ , we will apply the distributive property, also known as the FOIL method for binomials. This involves multiplying each term in the first binomial by each term in the second binomial.

Step 1: Multiply the first terms: $2y \times y = 2y^2$ .
Step 2: Multiply the outer terms: $2y \times -4 = -8y$ .
Step 3: Multiply the inner terms: $-3 \times y = -3y$ .
Step 4: Multiply the last terms: $-3 \times -4 = 12$ .

Next, we combine all these results: $2y^2 - 8y - 3y + 12$ .

Then, we combine the like terms $-8y$ and $-3y$ to get $-11y$ .

Therefore, the expanded expression is $2y^2 - 11y + 12$ .

This matches choice (3): $2y^2 - 11y + 12$ .

Thus, the solution to the problem is $2y^2 - 11y + 12$ .

Final Answer

$2y^2-11y+12$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiply systematically
Technique: $2y \times (-4) = -8y$ and $(-3) \times y = -3y$
Check: Combine like terms: $-8y + (-3y) = -11y$ ✓

Common Mistakes

Avoid these frequent errors

Sign errors when multiplying negative terms
Don't forget that (-3) × (-4) = +12, not -12! Students often lose track of negative signs during multiplication. Always track each sign carefully: negative × negative = positive, negative × positive = negative.

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 keep getting the wrong sign on my constant term?

This happens when you forget that negative times negative equals positive! In $(-3) \times (-4)$ , both numbers are negative, so the result is positive 12, not negative 12.

What's the easiest way to remember FOIL?

First terms, Outer terms, Inner terms, Last terms. For $(2y-3)(y-4)$ : First = $2y \cdot y$ , Outer = $2y \cdot (-4)$ , Inner = $(-3) \cdot y$ , Last = $(-3) \cdot (-4)$ .

How do I combine the middle terms correctly?

Add the coefficients of like terms: $-8y + (-3y) = -8y - 3y = -11y$ . Remember that adding a negative is the same as subtracting!

Can I check my answer by substituting a value?

Yes! Pick any value for y (like y = 1). Check: $(2(1)-3)(1-4) = (-1)(-3) = 3$ and $2(1)^2-11(1)+12 = 2-11+12 = 3$ . Both equal 3 ✓

What if I get confused with all the negative signs?

Write each step clearly and use parentheses! For example: $2y^2 + (-8y) + (-3y) + 12$ . This makes it easier to see that you're adding negative terms.

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