Expand (x-2)(x+5): Converting to Standard Quadratic Form

Polynomial Expansion with FOIL Method

Find the standard representation of the following function

f(x)=(x−2)(x+5) f(x)=(x-2)(x+5)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplified to the standard representation of the function
00:03 Open parentheses properly, multiply each factor by each factor
00:18 Collect terms
00:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the standard representation of the following function

f(x)=(x−2)(x+5) f(x)=(x-2)(x+5)

2

Step-by-step solution

We will begin by using the distributive property in order to expand the following expression.

(a+1)⋆(b+2) = ab+2a+b+2

We will then proceed to insert the known values into the equation and solve as follows:

(x-2)(x+5) =

x²-2x+5x+-2*5=

x²+3x-10

And that's the solution!

3

Final Answer

f(x)+x2+3x−10 f(x)+x^2+3x-10

Key Points to Remember

Essential concepts to master this topic
  • FOIL Rule: First, Outer, Inner, Last terms multiply systematically
  • Technique: (x-2)(x+5) = x² + 5x - 2x - 10
  • Check: Combine like terms: 5x - 2x = 3x gives x² + 3x - 10 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to multiply the constant terms
    Don't skip multiplying (-2) × (+5) = -10! This leaves out the constant term completely. The Last step in FOIL is crucial - you need all four products. Always multiply First, Outer, Inner, AND Last terms.

Practice Quiz

Test your knowledge with interactive questions

Create an algebraic expression based on the following parameters:

\( a=2,b=2,c=2 \)

FAQ

Everything you need to know about this question

What does FOIL stand for exactly?

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FOIL helps you remember the four multiplications needed:

  • First: x × x = x²
  • Outer: x × 5 = 5x
  • Inner: (-2) × x = -2x
  • Last: (-2) × 5 = -10

Why do I get -10 instead of +10?

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Pay attention to the signs! When you multiply (-2) × (+5), you get negative 10. The negative sign from the first binomial carries through the multiplication.

How do I combine 5x and -2x?

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These are like terms because they both have x to the first power. Simply add the coefficients: 5x+(−2x)=3x 5x + (-2x) = 3x

Can I use a different method besides FOIL?

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Yes! You can use the distributive property twice: distribute x from the first binomial, then distribute -2. FOIL is just a shortcut for this process.

What if I mess up the order of terms?

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The final order doesn't matter as long as you have all terms! Whether you write x2+3x−10 x² + 3x - 10 or 3x+x2−10 3x + x² - 10 , both are correct. Standard form puts the highest power first.

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