Question

factorise (a+b)^3 - (b+c)^3 + (c+a)^3 + 3(a+b)(b+c)(c+a)

Answer 1

(ᴀ-ʙ)3 + (ʙ-ᴄ)3 + (ᴄ-ᴀ)3 = ᴀ3 - ʙ3 - 3ᴀʙ(ᴀ-ʙ) + ʙ3 - ᴄ3 - 3ʙᴄ(ʙ-ᴄ) + ᴄ3 - ᴀ3 - 3ᴄᴀ(ᴄ-ᴀ)

= - 3ᴀ2ʙ + 3ᴀʙ2 - 3ʙ2ᴄ + 3ʙᴄ2 - 3ᴀᴄ2 + 3 ᴀ2ᴄ = 3 (- ᴀ2ʙ + ᴀʙ2 - ʙ2ᴄ + ʙᴄ2 - ᴀᴄ2 + ᴀ2ᴄ)

= 3 [(ᴀ2(ᴄ-ʙ) + (ʙ2(ᴀ-ᴄ) + (ᴄ2(ʙ-ᴀ)]

ᴏʀ

ʟᴇᴛ x = (ᴀ – ʙ), ʏ = (ʙ – ᴄ) ᴀɴᴅ ᴢ = (ᴄ – ᴀ)

ᴄᴏɴsɪᴅᴇʀ, x + ʏ + ᴢ = (ᴀ – ʙ) + (ʙ – ᴄ) + (ᴄ – ᴀ) = 0

⇒ x3 + ʏ3 + ᴢ3 = 3xʏᴢ

ᴛʜᴀᴛ ɪs (ᴀ – ʙ)3 + (ʙ – ᴄ)3 + (ᴄ – ᴀ)3 = 3(ᴀ – ʙ)(ʙ – ᴄ)(ᴄ – ᴀ)

Answer 2

Answer:

Refers to the attachment