Fill the blank so the statement is true: 9y² − ____ + 25 = (3y − 5)².

Fill the blank so the statement is true: $9 y^{2}$ − ____ + $25 = (3 y - 5)^{2}$ .

Class 8Algebraic Expressions and IdentitiesAlgebra

(3 y - 5)^{2} = (3 y)^{2} - 2 (3 y) (5) + 5^{2} = 9 y^{2} - 30 y + 25

, so the blank is

30 y

. Writing

15 y

forgets the factor 2 in

2 ab

;

60 y

doubles it once too often;

8 y

comes from adding 3 + 5 instead of multiplying.

Answer: C)

30 y

Combine **like terms only** — same variables and same powers.

Example:

(3 x^{2} + 4 x - 2) + (5 x^{2} - 7 x + 8) = (3 x^{2} + 5 x^{2}) + (4 x - 7 x) + (- 2 + 8) = 8 x^{2} - 3 x + 6

.

For subtraction, distribute the minus sign first:

(3 x^{2} + 4 x) - (x^{2} - 2 x) = 3 x^{2} + 4 x - x^{2} + 2 x = 2 x^{2} + 6 x

Don't just memorise the answer — build a daily practice habit.