Example 3 - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)

Transcript

Example 3 Expand (𝑎+𝑏)(𝑎^2+2𝑎𝑏+𝑏^2 ).Solving (𝑎+𝑏)(𝑎^2+2𝑎𝑏+𝑏^2 ) = 𝑎(𝑎^2+2𝑎𝑏+𝑏^2 )+𝑏(𝑎^2+2𝑎𝑏+𝑏^2 ) = 𝑎 × 𝑎^2+𝑎 × 2𝑎𝑏+𝑎 × 𝑏^2+𝑏 × 𝑎^2+𝑏 × 2𝑎𝑏+𝑏 × 𝑏^2 = 𝑎^3+𝑎 × 𝑎 × 2𝑏+𝑎𝑏^2+𝑏𝑎^2+𝑏 × 𝑏 × 2𝑎+𝑏^3 = 𝑎^3+𝑎^2 × 2𝑏+𝑎𝑏^2+𝑏𝑎^2+𝑏^2 × 2𝑎+𝑏^3 = 𝒂^𝟑+𝟐𝒃𝒂^𝟐 +𝒂𝒃^𝟐+𝒃𝒂^𝟐+𝟐𝒂𝒃^𝟐 +𝒃^𝟑 Adding like terms together = 𝑎^3+(2𝑏𝑎^2+𝑏𝑎^2)+(2𝑎𝑏^2+𝑎𝑏^2)+𝑏^3 = 𝒂^𝟑+𝟑𝒃𝒂^𝟐+𝟑𝒂𝒃^𝟐+𝒃^𝟑 This is a common identity (𝑎+𝑏)(𝑎^2+2𝑎𝑏+𝑏^2 )=(𝑎+𝑏) ×(𝑎+𝑏)^2 =(𝒂+𝒃)^𝟑 =𝒂^𝟑+𝟑𝒃𝒂^𝟐+𝟑𝒂𝒃^𝟐+𝒃^𝟑