Which expansion is correct: (2x + 1)² = ?

4x² + 4x + 1. (a+b)² = a² + 2ab + b² with a = 2x, b = 1: (2x)² + 2(2x)(1) + 1² = 4x² + 4x + 1.

Which expansion is correct: $(2 x + 1)^{2}$ = ?

Class 8Algebraic Expressions and IdentitiesAlgebra

(a + b)^{2} = a^{2} + 2 ab + b^{2}

with

a = 2 x, b = 1 : (2 x)^{2} + 2 (2 x) (1) + 1^{2} = 4 x^{2} + 4 x + 1

Answer: A)

4 x^{2} + 4 x + 1

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.