Verify the Equality: (2x-3)(-4+y) = -8x+2xy-3y+12

Q: Why do I need to multiply every term by every other term?

The distributive property requires each term in the first binomial to be multiplied by each term in the second binomial. Missing any combination gives an incomplete result!

Q: Does the order of terms in my final answer matter?

No! $ -8x + 2xy - 3y + 12 $ equals $ 2xy - 8x + 12 - 3y $. You can rearrange terms in any order since addition is commutative.

Q: How do I remember the FOIL method?

First terms, Outer terms, Inner terms, Last terms. For $ (2x-3)(-4+y) $: First: $ 2x \times (-4) $, Outer: $ 2x \times y $, Inner: $ (-3) \times (-4) $, Last: $ (-3) \times y $

Q: What if I get confused with negative signs?

Take it step by step! Remember: negative times negative equals positive $ (-3) \times (-4) = +12 $, but negative times positive equals negative $ (-3) \times y = -3y $.

Q: Can I check my work without expanding the other side?

Yes! Substitute simple values like $ x = 1, y = 0 $ into both sides. If $ (2(1)-3)(-4+0) = -8(1)+2(1)(0)-3(0)+12 $ gives the same result, you're correct!

Polynomial Distribution with Binomial Factors

Is equality correct?

$(2x-3)(-4+y)=-8x+2xy-3y+12$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Are the expressions equal?

00:04 Let's properly open parentheses, multiply each factor by each factor

00:25 Let's calculate the products

00:40 Let's compare the terms of the expressions, we'll see they're equal

00:47 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

Is equality correct?

$(2x-3)(-4+y)=-8x+2xy-3y+12$

Step-by-step solution

To solve this problem, we'll perform the distribution as follows:

Distribute the term $(2x-3)$ across $(-4+y)$ .
Calculate $(2x) \times (-4)$ and $(2x) \times y$ .
Calculate $(-3) \times (-4)$ and $(-3) \times y$ .

Let's compute these multiplications:

Let us expand the left side using distribution:
$(2x - 3)(-4 + y)$
= $(2x)(-4) + (2x)(y) + (-3)(-4) + (-3)(y)$
= $-8x + 2xy + 12 - 3y$ .

After simplification, the expression becomes:

$-8x + 2xy - 3y + 12$ .

Comparing this with the right-hand side of the original equation $-8x + 2xy - 3y + 12$ , we observe that both sides are equal.

Therefore, the two sides of the equation are equal, confirming that the given equality is correct.

The final solution is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms when multiplying binomials
Technique: $(2x)(-4) = -8x$ and $(-3)(y) = -3y$
Check: Rearrange terms to match given expression order ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute all terms
Don't multiply just the first term of each binomial = incomplete expansion! This gives you only part of the answer and misses crucial terms. Always multiply every term in the first binomial by every term in the 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 need to multiply every term by every other term?

The distributive property requires each term in the first binomial to be multiplied by each term in the second binomial. Missing any combination gives an incomplete result!

Does the order of terms in my final answer matter?

No! $-8x + 2xy - 3y + 12$ equals $2xy - 8x + 12 - 3y$ . You can rearrange terms in any order since addition is commutative.

How do I remember the FOIL method?

First terms, Outer terms, Inner terms, Last terms. For $(2x-3)(-4+y)$ : First: $2x \times (-4)$ , Outer: $2x \times y$ , Inner: $(-3) \times (-4)$ , Last: $(-3) \times y$

What if I get confused with negative signs?

Take it step by step! Remember: negative times negative equals positive $(-3) \times (-4) = +12$ , but negative times positive equals negative $(-3) \times y = -3y$ .

Can I check my work without expanding the other side?

Yes! Substitute simple values like $x = 1, y = 0$ into both sides. If $(2(1)-3)(-4+0) = -8(1)+2(1)(0)-3(0)+12$ gives the same result, you're correct!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Algebraic Technique questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime