Question

CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. x² + 10xy + 25y² A. (x + 5y) (x - 5y) b. x² - 10xy + 25y² B. (x + 5y)² c. x² - 25y² C. (x - 5y)² d. 25y² - x² D. (5y + x) (5y - x)

Accepted Answer

Identify the type of polynomial for each expression in Column I. Notice that these are quadratic expressions in terms of x and y, and some resemble perfect square trinomials or difference of squares. Recall the formulas for factoring: 
- Perfect square trinomial: $$a^2 + 2ab$$ + $$b^2 = (a$$ + $$b)^2
- $$Perfect square trinomial with subtraction: $$a^2 - 2ab$$ + $$b^2 = (a$$ - $$b)^2
- $$Difference of squares: $$a^2$$ - $$b^2 = (a + b)(a - b$$)$$ For expression a: x^2$ + 10xy + 25y^2$, recognize it as a perfect square trinomial where a = x$ and b = 5y$. Use the formula a^2$ + 2ab + b^2$ = (a + b)^2$ to factor it. For expression b: x^2$ - 10xy + 25y^2$, recognize it as a perfect square trinomial with subtraction, where a = x$ and b = 5y$. Use the formula a^2$ - 2ab + b^2$ = (a - b)^2$ to factor it. For expressions c and d, identify them as difference of squares: 
- For c: x^2$ - 25y^2$, write it as a^2$ - b^2$ with a = x$ and b = 5y$.
- For d: 25y^2$ - x^2$, write it as a^2$ - b^2$ with a = 5y$ and b = x$.
Then factor both using a^2$ - b^2$ = (a + b)(a - b).$$

CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. x² + 10xy + 25y² A. (x + 5y) (x - 5y) b. x² - 10xy + 25y² B. (x + 5y)² c. x² - 25y² C. (x - 5y)² d. 25y² - x² D. (5y + x) (5y - x)

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Key Concepts

Factoring Perfect Square Trinomials

Difference of Squares

Matching Polynomials to Factored Forms