Verify if a²+9a-20 Equals (a+4)(a-5): Equation Check

Q: How do I remember the FOIL method correctly?

FOIL stands for First, Outer, Inner, Last. For $ (a+4)(a-5) $: First = $ a \times a $, Outer = $ a \times (-5) $, Inner = $ 4 \times a $, Last = $ 4 \times (-5) $

Q: Why did I get +9a instead of -a?

This happens when you make a sign error during multiplication or combining like terms. Remember: $ -5a + 4a = -a $, not $ +9a $. Always double-check your signs!

Q: Can I expand binomials without FOIL?

Yes! You can use the distributive property twice: $ (a+4)(a-5) = a(a-5) + 4(a-5) $. Both methods give the same answer when done correctly.

Q: What if I keep making arithmetic mistakes?

Write out every single step and don't skip any. Use parentheses to keep track of signs: $ (-5a) + (+4a) = -a $. Going slower prevents careless errors!

Polynomial Expansion with Sign Verification

Is the equation correct?

$a^2+9a-20=(a+4)(a-5)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Are the expressions equal?

00:03 Let's properly open parentheses and multiply each factor by each factor

00:20 Let's calculate the products

00:29 Let's compare the terms of the expressions

00:38 Let's group the factors

00:42 We can see that the expressions are not equal due to coefficient A

00:49 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 the equation correct?

$a^2+9a-20=(a+4)(a-5)$

Step-by-step solution

We solve the right side of the equation using the extended distributive property: $(a+b)\times(c+d)=ac+ad+bc+bd$

$(a+4)(a-5)=a^2-5a+4a-20$

$a^2-a-20$

That is, answer D is the correct one.

Final Answer

No, $-a$ instead of $+9a$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: Multiply first, outer, inner, last terms systematically
Technique: $(a+4)(a-5) = a^2 - 5a + 4a - 20$
Check: Combine like terms and compare coefficients: $a^2 - a - 20$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly combining like terms or sign errors
Don't rush through $-5a + 4a$ and write $+9a$ = wrong coefficient! This happens when you add instead of subtract or flip signs. Always carefully track positive and negative signs when combining like terms.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

How do I remember the FOIL method correctly?

FOIL stands for First, Outer, Inner, Last. For $(a+4)(a-5)$ : First = $a \times a$ , Outer = $a \times (-5)$ , Inner = $4 \times a$ , Last = $4 \times (-5)$

Why did I get +9a instead of -a?

This happens when you make a sign error during multiplication or combining like terms. Remember: $-5a + 4a = -a$ , not $+9a$ . Always double-check your signs!

Can I expand binomials without FOIL?

Yes! You can use the distributive property twice: $(a+4)(a-5) = a(a-5) + 4(a-5)$ . Both methods give the same answer when done correctly.

How do I check if my expansion is correct?

Compare your expanded form with the original expression term by term. The coefficients of like terms must match exactly. If they don't, re-expand carefully.

What if I keep making arithmetic mistakes?

Write out every single step and don't skip any. Use parentheses to keep track of signs: $(-5a) + (+4a) = -a$ . Going slower prevents careless errors!

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