Identities in algebra can sometimes be shown as area relationships. For example: Class 9

Identities in algebra can sometimes be shown as area relationships. For example: Class 9

In the problems below, unless stated otherwise, use the approximation $\frac{22}{7}$ for π.

Question 1.

Identities in algebra can sometimes be shown as area relationships. For example: Class 9

The figure shown corresponds to the identity

(a + b)² = a² + 2ab + b².

Do you see how?

Draw figures corresponding to the identities (a + b) (a- b) = a² - b² and

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

Solution:

Side of bigger square = (a + b)

∴ Total area of bigger square = (a + b)²

Dividing the square into 4 parts

Area of square with side a = a²

∵ Area of square with side b = b²

∵ Two rectangles each of area ab

∴ Total area = a² + ab + ab + b²

= a² + 2ab + b²

∴ (a + b)² = a² + 2ab + b²

i. Identity: (a + b)(a - b) = a² - b²

ii. Identity: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca