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Find $k$ so that $9 a^{2} - 30 ab + k b^{2}$ is a perfect square.

Class 9Algebraic IdentitiesPolynomials

A5
B100
C25
D15

Step-by-Step Solution

(3 a - 5 b)^{2} = 9 a^{2} - 30 ab + 25 b^{2}

, so

k = 25

. The middle term

- 30 ab = - 2 (3 a) (5 b)

fixes the 5.

Answer: C) 25

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