Q. Use the distributive property to expand \(8(x+3)\).

Q: What is the expanded form of 8(x+3)?.

8(x+3)=8x+24. Multiply 8 by each term inside the parentheses.

Q: Why do we multiply 8 by both x and 3?

By the distributive property: a(b+c)=ab+ac. So 8(x+3)=8\cdot x+8\cdot 3. .

Q: How would a negative outside affect the result, e.g., -8(x+3)?

Multiply the negative: -8(x+3)=-8x-24. The sign distributes with the coefficient.

Q: How do I check my expansion is correct?

Pick a value (e.g., x=2). Evaluate both: 8(2+3)=8\cdot5=40 and 8\cdot2+24=16+24=40. They match.

Q: Can I reverse the process (factor) 8x+24 back to parentheses?.

Yes: factor out the common factor 8: 8x+24=8(x+3).

Q: What if the parentheses contain subtraction, like 8(x-3)?.

What if the parentheses contain subtraction, like 8(x-3)?.

Q: How do you distribute with fractions, e.g., \tfrac12(x+3) ?

Multiply each term: \tfrac12(x+3)=\tfrac12 x+\tfrac32..

Q: Can you distribute an exponent over addition, like (x+3)^2 ?

No. (x+3)^2 \neq x^2+3^2 . Use FOIL or expansion: (x+3)^2=x^2+6x+9 .

Answer

\(8(x+3)=8\cdot x+8\cdot 3=8x+24\)

Detailed Explanation

Step-by-step explanation using the distributive property

State the distributive property (general form): the product of a number and a sum equals the sum of the products. In symbolic form: \(a(b+c)=ab+ac\).
Identify the parts in the given expression \(8(x+3)\). Here \(a=8\), \(b=x\), and \(c=3\).
Apply the distributive property by multiplying 8 by each term inside the parentheses separately: \(8(x+3)=8\cdot x+8\cdot 3\).
Simplify each product. Multiplying 8 by \(x\) gives \(8x\). Multiplying 8 by 3 gives 24. So the expression becomes \(8x+24\).
Write the final expanded form: \(8(x+3)=8x+24\).

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Algebra FAQs

What is the expanded form of \(8(x+3)\)?.

\(8(x+3)=8x+24\). Multiply 8 by each term inside the parentheses.

Why do we multiply 8 by both \(x\) and \(3\)?

By the distributive property: \(a(b+c)=ab+ac\). So \(8(x+3)=8\cdot x+8\cdot 3\). .

How would a negative outside affect the result, e.g., \(-8(x+3)\)?

Multiply the negative: \(-8(x+3)=-8x-24\). The sign distributes with the coefficient.

How do I check my expansion is correct?

Pick a value (e.g., \(x=2\)). Evaluate both: \(8(2+3)=8\cdot5=40\) and \(8\cdot2+24=16+24=40\). They match.

Can I reverse the process (factor) \(8x+24\) back to parentheses?.

Yes: factor out the common factor 8: \(8x+24=8(x+3)\).

What if the parentheses contain subtraction, like \(8(x-3)\)?.

How do you distribute with fractions, e.g., \( \tfrac12(x+3) \)?

Multiply each term: \(\tfrac12(x+3)=\tfrac12 x+\tfrac32\)..

Can you distribute an exponent over addition, like \( (x+3)^2 \)?

No. \( (x+3)^2 \neq x^2+3^2 \). Use FOIL or expansion: \( (x+3)^2=x^2+6x+9 \) .

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