Verify the Expansion: (x+8)(2x-3) = 2x²+13x-24

Q: What does FOIL stand for and why use it?

FOIL stands for First, Outer, Inner, Last. It's a systematic way to multiply two binomials without missing any terms. Each letter reminds you which terms to multiply together!

Q: How do I know if I combined the middle terms correctly?

The middle terms come from Outer and Inner in FOIL. Here: $ x \cdot (-3) = -3x $ and $ 8 \cdot 2x = 16x $, so $ -3x + 16x = 13x $.

Q: What if I get a different constant term?

The constant term comes from multiplying the Last terms: $ 8 \cdot (-3) = -24 $. If you get $ +24 $, you missed the negative sign!

Q: Can I expand binomials without FOIL?

Yes! You can use the distributive property twice: $ (x+8)(2x-3) = x(2x-3) + 8(2x-3) $. FOIL is just a shortcut for the same process.

Q: How do I check if two expressions are equal?

Expand the left side completely, then compare each coefficient with the right side. The $ x^2 $, $ x $, and constant terms must all match exactly.

Binomial Expansion with FOIL Verification

Is equality correct?

$(x+8)(2x-3)=2x^2+13x-24$

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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

00:20 Let's calculate the products

00:35 Let's group the factors

00:44 Let's compare the terms of the expressions, and see that they are equal

00:48 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?

$(x+8)(2x-3)=2x^2+13x-24$

Step-by-step solution

To solve this problem, we'll confirm whether $(x+8)(2x-3) = 2x^2+13x-24$ is a true equality by expanding and simplifying the left-hand expression.

Step 1: Use the FOIL method to expand $(x+8)(2x-3)$ .

First: Multiply the first terms: $x \cdot 2x = 2x^2$ .
Outer: Multiply the outer terms: $x \cdot (-3) = -3x$ .
Inner: Multiply the inner terms: $8 \cdot 2x = 16x$ .
Last: Multiply the last terms: $8 \cdot (-3) = -24$ .

Step 2: Combine these results:

$2x^2 + (-3x) + 16x + (-24) = 2x^2 + 13x - 24$

Step 3: Compare with the right-hand side:

The expanded form is $2x^2 + 13x - 24$ , which matches the right side of the original equation.

Therefore, the expression $(x+8)(2x-3)$ correctly simplifies to $2x^2 + 13x - 24$ , verifying the equality.

Thus, the correct answer is: Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiply systematically
Technique: $x \cdot 2x = 2x^2$ , then $-3x + 16x = 13x$
Check: Expanded form must match given expression exactly ✓

Common Mistakes

Avoid these frequent errors

Sign errors when combining like terms
Don't forget negative signs when multiplying = wrong middle term! Students often get $-3x + 16x = 19x$ instead of $13x$ . Always track positive and negative signs carefully through each FOIL step.

Practice Quiz

Test your knowledge with interactive questions

It is possible to use the distributive property to simplify the expression below?

What is its simplified form?

$$ (ab)(c d) $$

$$

FAQ

Everything you need to know about this question

What does FOIL stand for and why use it?

FOIL stands for First, Outer, Inner, Last. It's a systematic way to multiply two binomials without missing any terms. Each letter reminds you which terms to multiply together!

How do I know if I combined the middle terms correctly?

The middle terms come from Outer and Inner in FOIL. Here: $x \cdot (-3) = -3x$ and $8 \cdot 2x = 16x$ , so $-3x + 16x = 13x$ .

What if I get a different constant term?

The constant term comes from multiplying the Last terms: $8 \cdot (-3) = -24$ . If you get $+24$ , you missed the negative sign!

Can I expand binomials without FOIL?

Yes! You can use the distributive property twice: $(x+8)(2x-3) = x(2x-3) + 8(2x-3)$ . FOIL is just a shortcut for the same process.

How do I check if two expressions are equal?

Expand the left side completely, then compare each coefficient with the right side. The $x^2$ , $x$ , and constant terms must all match exactly.

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