Question

Factorise
Please with full method

Answer 1

Explanation:

`Remember:\\\\\boxed{x^3-y^3=(x-y)(x^2+xy+y^2)}\\\\64a^3-(b-c)^3\\\\=(4a)^3-(b-c)^3\\\\=(4a-(b-c))(16a^2+4a(b-c)+(b-c)^2)\\\\=(4a-b+c)(16a^2+4ab-4ac+b^2-2bc+c^2)\\`

Answer 2

`\boxed{\sf (a-b)^3=a^3-3a^2b+3ab^2-b^3}`

`\\ \sf\longmapsto 64a^3-(b-c)^3`

`\\ \sf\longmapsto 64a^3-(b^3-3b^2c+3bc^2-c^3)`

`\\ \sf\longmapsto 64a^3-b^3+3b^2c-3bc^2+c^3`

`\\ \sf\longmapsto 64a^3-b^3+c^3+3b^2c-3bc^2`