Question

What polynomial, when factored, gives (3x + 5y) (3x - 5y)?

Answer 1

`9x^2 - 25y^2`

Explanation:

• The polynomial that, when factored, gives ( 3x + 5y )( 3x - 5y ) is:

`\sf (3x + 5y)(3x - 5y) = (3x)^2 - (5y)^2`

• Using the difference of squares formula:

`\sf (a^2 - b^2) = (a + b)(a - b)`

• we can simplify further:

`\sf (3x + 5y)(3x - 5y) \\\\ (3x)^2 - (5y)^2 \\\\ 9x^2 - 25y^2`

• Therefore, the polynomial that, when factored, gives

`\sf (3x + 5y)(3x - 5y) = 9x^2 - 25y^2`

Answer 2

• 9x² - 25y²

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We can observe it is a special form of the difference of squares identity:

• a² - b² = (a + b)(a - b),

where a = 3x and b = 5y

Therefore the polynomial is:

• (3x)² - (5y)² =
• 9x² - 25y²