Neha writes (2x + 3)² = 4x² + 9. Substituting x = 1 into both sides, what does the check show?

Neha writes $(2 x + 3)^{2} = 4 x^{2} + 9$ . Substituting $x = 1$ into both sides, what does the check show?

Class 8Algebraic Expressions and IdentitiesAlgebra

x = 1

the left side is

(2 + 3)^{2} = 25

, while Neha's right side gives 4 + 9 = 13. The sides disagree, so her expansion is wrong. The correct one is

(2 x + 3)^{2} = 4 x^{2} + 2 (2 x) (3) + 9 = 4 x^{2} + 12 x + 9

, which at

x = 1

gives 4 + 12 + 9 = 25 and matches.

(a + b)^{2}

always carries a middle term.

Answer: B) Left side is 25 but right side is 13 — the middle term

12 x

is missing

Identities save time and reveal structure. Examples of clever uses:

- Compute

10 2^{2}

mentally:

(100 + 2)^{2} = 10 0^{2} + 2 (100) (2) + 2^{2} = 10000 + 400 + 4 = 10404

.
- Compute

99 \times 101 : (100 - 1) (100 + 1) = 10 0^{2} - 1^{2} = 10000 - 1 = 9999

.
- Compute

4 7^{2} - 4 3^{2} : (47 - 43) (47 + 43) = 4 \times 90 = 360

.

Look at any number-pair calculation; if you can rewrite it as one of the three identity forms, the answer falls out.

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