Example 7 - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)

Transcript

Example 7 Find factors of 50𝑝^2+60𝑝𝑞+18𝑞^2. What will 𝑎 and 𝑏 be in this case? Here, 50 isn’t the square of any number Similarly, 18 isn’t the square of any number So, to factorise this expression, we take some common factors out 𝟓𝟎𝒑^𝟐+𝟔𝟎𝒑𝒒+𝟏𝟖𝒒^𝟐 = 2 × 25𝑝^2+2 × 30𝑝𝑞+2 × 9𝑞^2 = 𝟐 × [𝟐𝟓𝒑^𝟐+𝟑𝟎𝒑𝒒+𝟗𝒒^𝟐 ] = 2 × [25𝑝^2+9𝑞^2+30𝑝𝑞] Since 25 = 52, 9 = 32, we can write our expression as Taking 2 common as all have common factor 2 Since 25 = 52, 9 = 32, we can factorise our expression = 2 × [(𝟓𝒑)^𝟐+(𝟑𝒒)^𝟐+𝟐 × 𝟓𝒑 × 𝟑𝒒] = 𝟐 ×(𝟓𝒑+𝟑𝒒)^𝟐 Using (𝑎+𝑏)^2 = 𝑎^2 + 𝑏^2 + 2ab Where 𝑎 = 5𝑝, b = 3𝑞