Which statement shows how the product of $(x+5)^2$ demonstrates the closure property of multiplication?

A. $x^2 + 25$ is a polynomial
B. $x^2 + 25$ may or may not be a polynomial
C. $x^2 + 10x + 25$ is a polynomial
D. [tex]$x^2 + 10x + 25$[/tex] may or may not be a polynomial

Sure, let's solve this step-by-step to determine which statement correctly shows how the product of $(x+5)^2$ demonstrates the closure property of multiplication.

1. First, expand the expression $(x+5)^2$:
[tex]\[ (x + 5)^2 = (x + 5)(x + 5) \][/tex]

2. Next, use the distributive property to expand the product:
[tex]\[ (x + 5)(x + 5) = x(x + 5) + 5(x + 5) \][/tex]

3. Distribute the terms inside the parentheses:
[tex]\[ x(x + 5) = x^2 + 5x \][/tex]
[tex]\[ 5(x + 5) = 5x + 25 \][/tex]

4. Combine all the terms together:
[tex]\[ x^2 + 5x + 5x + 25 \][/tex]

5. Combine like terms:
[tex]\[ x^2 + 10x + 25 \][/tex]

The final expanded polynomial is:
[tex]\[ x^2 + 10x + 25 \][/tex]

This shows that $(x+5)^2$ expands to $x^2 + 10x + 25$, which is indeed a polynomial. This demonstrates the closure property of multiplication, which states that the product of two polynomials is also a polynomial.

By examining the options, we're choosing the one that correctly reflects this polynomial:

$x^2 + 10x + 25$ is a polynomial.

Therefore, the correct statement is:
[tex]\[ x^2 + 10x + 25 \text{ is a polynomial} \][/tex]

Which statement shows how the product of \((x+5)^2\) demonstrates the closure property of multiplication?A. \(x^2 + 25\) is a polynomialB. \(x^2 + 25\) may or may not be a polynomialC. \(x^2 + 10x + 25\) is a polynomialD. [tex]\(x^2 + 10x + 25\)[/tex] may or may not be a polynomial

Answer :

Other Questions

Which statement shows how the product of \((x+5)^2\) demonstrates the closure property of multiplication?

A. \(x^2 + 25\) is a polynomial
B. \(x^2 + 25\) may or may not be a polynomial
C. \(x^2 + 10x + 25\) is a polynomial
D. [tex]\(x^2 + 10x + 25\)[/tex] may or may not be a polynomial