Question

Take suitable number of cards given in the adjoining diagram [G(x × x) representing x², R(x × 1) representing x and Y(1 × 1) representing 1] to factorise the following expressions, by arranging the cards in the form of rectangles:

1. 2x² + 6x + 4
2. x² + 4x + 4.

Factorise 2x² + 6x + 4 by using the figure.

Calculate the area of figure.

Answer 1

i. 2x² + 6x + 4 = 2x² + 4x + 2x + 4

= 2x(x + 2) + 2(x + 2)

= (x + 2)(2x + 2)

= 2(x + 2)(x + 1)

ii. x² + 4x + 4 = x² + 2x + 2x + 4

= x² + 2x + 2x + 4

= x(x + 2) + 2(x + 2)

= (x + 2)(x + 2)