QuestionMay 4, 2026

Factor by grouping to obtain the difference of two squares. 9x^2-30x+25-36y^2 9x^2-30x+25-36y^2=square (Factor completely.)

Factor by grouping to obtain the difference of two squares. 9x^2-30x+25-36y^2 9x^2-30x+25-36y^2=square (Factor completely.)
Factor by grouping to obtain the difference of two squares.
9x^2-30x+25-36y^2
9x^2-30x+25-36y^2=square  (Factor completely.)

Solution
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Answer

(3x - 5 - 6y)(3x - 5 + 6y) Explanation 1. Group terms Group (9x^2 - 30x + 25) and (-36y^2) to prepare for factoring. 2. Factor quadratic in x 9x^2 - 30x + 25 is a perfect square trinomial: (3x - 5)^2. 3. Write as difference of squares Expression becomes (3x - 5)^2 - (6y)^2. 4. Apply difference of squares formula **a^2 - b^2 = (a - b)(a + b)** with a = (3x - 5), b = 6y. 5. Factor completely (3x - 5 - 6y)(3x - 5 + 6y).

Explanation

1. Group terms<br /> Group $(9x^2 - 30x + 25)$ and $(-36y^2)$ to prepare for factoring.<br />2. Factor quadratic in $x$<br /> $9x^2 - 30x + 25$ is a perfect square trinomial: $(3x - 5)^2$.<br />3. Write as difference of squares<br /> Expression becomes $(3x - 5)^2 - (6y)^2$.<br />4. Apply difference of squares formula<br /> **$a^2 - b^2 = (a - b)(a + b)$** with $a = (3x - 5)$, $b = 6y$.<br />5. Factor completely<br /> $(3x - 5 - 6y)(3x - 5 + 6y)$.
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