The big square has side (a + b) and is cut into four parts as shown. Which expression gives its total area?

Class 8Algebraic Expressions and IdentitiesAlgebra

Step-by-Step Solution

The parts are a square

a \times a

, two rectangles

a \times b

and a square

b \times b

. Adding them:

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

Answer: B)

a^{2} + 2 ab + b^{2}

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

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