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The square of side (a + b) is split into four parts as shown. What is its total area?

Class 9Algebraic IdentitiesPolynomials

A $a^{2} + 2 ab + b^{2}$
B $a^{2} + ab + b^{2}$
C $2 a + 2 b$
D $a^{2} + b^{2}$

Step-by-Step Solution

The parts are one

a \times a

square, two

a \times b

rectangles and one

b \times b

square:

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

is half the perimeter.)

Answer: A)

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

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