Break Down the Expression: Simplifying 5x² + 10 into Basic Terms

Factoring Expressions with Common Factors

Break down the expression into basic terms:

5x2+10 5x^2 + 10

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Step-by-step written solution

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1

Understand the problem

Break down the expression into basic terms:

5x2+10 5x^2 + 10

2

Step-by-step solution

To break down the expression 5x2+10 5x^2 + 10 , identify the common factors.

The first term is 5x2 5x^2 , which can be rewritten as 5xx 5\cdot x\cdot x .

The second term is 10 10 , which can be rewritten as 52 5\cdot 2 .

Notice that both terms share a common factor of 5 5 .

This allows the expression to be broken down to 5(x2)+10 5(x^2) + 10 , which translates to 5xx+10 5\cdot x\cdot x + 10 using common terms.

3

Final Answer

5xx+10 5\cdot x\cdot x+10

Key Points to Remember

Essential concepts to master this topic
  • Rule: Break down each term into its basic multiplication components
  • Technique: Rewrite 5x2 5x^2 as 5xx 5 \cdot x \cdot x to show individual factors
  • Check: Verify that 5xx+10 5 \cdot x \cdot x + 10 equals original expression ✓

Common Mistakes

Avoid these frequent errors
  • Incorrectly breaking down exponents
    Don't write 5x2 5x^2 as 5x5x 5x \cdot 5x = 25x2 25x^2 ! This multiplies the coefficient twice and changes the value. Always write x2 x^2 as xx x \cdot x and keep the coefficient separate.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

\( 4x^2 + 6x \)

FAQ

Everything you need to know about this question

What does 'breaking down into basic terms' mean?

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It means showing each part of the expression as separate multiplication factors. Instead of 5x2 5x^2 , write it as 5xx 5 \cdot x \cdot x to see all the individual pieces.

Why can't I write 5x² as 5x • 5x?

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Because 5x5x=25x2 5x \cdot 5x = 25x^2 , which is not equal to 5x2 5x^2 ! The exponent x2 x^2 means xx x \cdot x , not 5x5x 5x \cdot 5x .

Do I need to break down the constant 10 too?

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The question asks for basic terms, so you could write 10 as 25 2 \cdot 5 or 101 10 \cdot 1 , but it's usually fine to leave simple constants as they are unless specifically asked.

What if the expression had more terms?

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The same principle applies! Break down each term separately: 3x3+2x+7 3x^3 + 2x + 7 becomes 3xxx+2x+7 3 \cdot x \cdot x \cdot x + 2 \cdot x + 7 .

How do I know I've broken it down correctly?

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Multiply your broken-down version back together. If 5xx+10 5 \cdot x \cdot x + 10 gives you 5x2+10 5x^2 + 10 , then you did it right!

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