Expand (x+25)(x-1): Multiplying Binomials with Square Numbers

Q: Do I need to calculate 5² before using FOIL?

Yes, absolutely! Always simplify exponents first according to order of operations. $ 5^2 = 25 $, so you're really expanding $ (x+25)(x-1) $, not $ (x+5^2)(x-1) $.

Q: What if I forget to combine like terms at the end?

You'll get the wrong answer! After FOIL gives you $ x^2 - x + 25x - 25 $, you must combine $ -x + 25x = 24x $ to get the final $ x^2 + 24x - 25 $.

Q: How do I remember the FOIL method order?

First terms, Outer terms, Inner terms, Last terms. For $ (x+25)(x-1) $: F=$ x \cdot x $, O=$ x \cdot (-1) $, I=$ 25 \cdot x $, L=$ 25 \cdot (-1) $.

Q: Why is my middle term 24x and not 26x?

Check your signs carefully! The outer term is $ x \cdot (-1) = -x $ (negative), and the inner term is $ 25 \cdot x = +25x $ (positive). So: $ -x + 25x = 24x $.

Q: Can I check my answer somehow?

Yes! Pick a simple value like $ x = 0 $. Original: $ (0+25)(0-1) = 25(-1) = -25 $. Your answer: $ 0^2 + 24(0) - 25 = -25 $. They match! ✓

Binomial Expansion with Perfect Squares

Solve the following problem:

$(x+5^2)(x-1)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's calculate the power

00:08 Let's properly open parentheses, multiply each factor by each factor

00:25 Let's calculate the products

00:36 Let's group the factors

00:46 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 following problem:

$(x+5^2)(x-1)=$

Step-by-step solution

In order to solve the following problem, simplify the expression step by step:

Step 1: Compute $5^2$
The first part of the expression involves $5^2$ . We compute:
$\quad 5^2 = 25$
Step 2: Rewrite the expression
Substitute $5^2$ with $25$ in the expression:
$\quad (x + 25)(x - 1)$
Step 3: Apply the FOIL method
Expand the expression using the FOIL method:
First: $x \cdot x = x^2$
Outer: $x \cdot (-1) = -x$
Inner: $25 \cdot x = 25x$
Last: $25 \cdot (-1) = -25$
Step 4: Combine like terms
Combine all the terms:
$\quad x^2 - x + 25x - 25$
Combine $-x$ and $25x$ :
$\quad x^2 + 24x - 25$

Thus, the expanded expression is $x^2 + 24x - 25$ .

Therefore, the final solution is:

$x^2 + 24x - 25$

Final Answer

$x^2+24x-25$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Calculate exponents before multiplying binomials
FOIL Method: First $x \cdot x = x^2$ , Outer $x \cdot (-1) = -x$ , Inner $25 \cdot x = 25x$ , Last $25 \cdot (-1) = -25$
Check: Combine like terms correctly: $-x + 25x = 24x$ to get final answer ✓

Common Mistakes

Avoid these frequent errors

Forgetting to calculate the exponent first
Don't leave $5^2$ as is and try to multiply binomials = confusion and wrong coefficients! Students often get $x^2 + 4x - 5$ instead of the correct $x^2 + 24x - 25$ . Always calculate $5^2 = 25$ first, then expand $(x+25)(x-1)$ .

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Do I need to calculate 5² before using FOIL?

Yes, absolutely! Always simplify exponents first according to order of operations. $5^2 = 25$ , so you're really expanding $(x+25)(x-1)$ , not $(x+5^2)(x-1)$ .

What if I forget to combine like terms at the end?

You'll get the wrong answer! After FOIL gives you $x^2 - x + 25x - 25$ , you must combine $-x + 25x = 24x$ to get the final $x^2 + 24x - 25$ .

How do I remember the FOIL method order?

First terms, Outer terms, Inner terms, Last terms. For $(x+25)(x-1)$ : F= $x \cdot x$ , O= $x \cdot (-1)$ , I= $25 \cdot x$ , L= $25 \cdot (-1)$ .

Why is my middle term 24x and not 26x?

Check your signs carefully! The outer term is $x \cdot (-1) = -x$ (negative), and the inner term is $25 \cdot x = +25x$ (positive). So: $-x + 25x = 24x$ .

Can I check my answer somehow?

Yes! Pick a simple value like $x = 0$ . Original: $(0+25)(0-1) = 25(-1) = -25$ . Your answer: $0^2 + 24(0) - 25 = -25$ . They match! ✓

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