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

$(3+20)\times(12+4)=$

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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