Which of the following expressions is the factored form of x3+125y3 ?(1 point) Responses (x2+5y2)(x2−5xy+25y2) open paren x squared plus 5 y squared close paren times open paren x squared minus 5 x y plus 25 y squared close paren (x+5y)(x2−5xy+25y2) open paren x plus 5 y close paren times open paren x squared minus 5 x y plus 25 y squared close paren (x−5y)(x2+5xy+25y2)

Answer 1

To factor the expression \( x^3 + 125y^3 \), we recognize that it can be expressed as a sum of cubes. The formula for factoring a sum of cubes is:

\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]

In this case, we can identify \( a = x \) and \( b = 5y \) since \( 125y^3 = (5y)^3 \).

Using the formula, we get:

1. Calculate \( a + b \): \[ x + 5y \]

2. Calculate \( a^2 \): \[ x^2 \]

3. Calculate \( ab \): \[ x \cdot 5y = 5xy \]

4. Calculate \( b^2 \): \[ (5y)^2 = 25y^2 \]

Substituting these into the formula yields:

\[ x^3 + 125y^3 = (x + 5y)(x^2 - 5xy + 25y^2) \]

Thus, the factored form of the expression \( x^3 + 125y^3 \) is:

\[ (x + 5y)(x^2 - 5xy + 25y^2) \]

Therefore, the correct response is:

(x + 5y)(x² - 5xy + 25y²).