Example 9 - More Identities - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)

Transcript

Example 9 Use this identity to find the square of a number, say 119 We have to use the identity (𝒂+𝒃+𝒄)^𝟐=𝒂^𝟐+𝒃^𝟐+𝒄^𝟐+𝟐𝒂𝒃+𝟐𝒃𝒄+𝟐𝒂𝒄 We write 119 as a sum of 3 numbers whose square is easy to find So, we can write 119 = 100 + 10 + 9 Now, finding square 〖𝟏𝟏𝟗〗^𝟐=(𝟏𝟎𝟎+𝟏𝟎+𝟗)^𝟐 Using (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑎𝑐 Putting 𝑎 = 100, 𝑏 = 10 & 𝑐 = 9 =100^2+10^2+9^2+2 × 100 × 10+2 × 100 × 9+2 × 10 × 9 =10,000+100+81+2,000+1,800+180 =10,000+100+81+2,000+1,800+180 =𝟏𝟒,𝟏𝟔𝟏